I've wondered this, and thus I've recently started a project to find out the answer to that question. I'm going to be doing a quick playthrough with each faction (or until I get bored ), trying to get a feel for how strong and effective the character is, then report my findings here, just in case people are curious.
The process is simple: Each faction will be evaluated, examined and looked at to see what skills seem to be most important for that faction. For instance, the Followers of the Apocalypse would be good at medicine and science, whereas the NCR would be good with guns and explosives. The skills that the faction specializes in would reflect onto their SPECIAL. Again, as an example, the Followers being good at Medicine and Science would raise their Intelligence, whereas the NCR would see a boost to their perception and Agility thanks to guns and explosives. STR is often governed by providing the character with the minimal STR neccesary to use all weapons utilized by that faction at optimal performance, UNLESS the faction is explicitly known for being exceptionally strong or specializes in Melee weapons (Great Khans and the Legion), or possibly if the faction has SPECIAL points to spare. Luck would be decided by the position of power that the faction finds itself in (or a lack thereof) and in the NCR's case, their luck on the Strip. For example, a White Glove Society member (supporting Mr. House) would have high luck due to Mr. House's luck of needing BOTH the NCR and Legion present to buy time to carry out his plans, whereas the NCR and Legion would see a drop in their luck because that same situation is unfortunate for them. Charisma would be decided by the faction's political relations, the amount of speech checks involved with that faction and by the faction's members' charisma. As an example, this would mean the Kings and the Followers would have a nice Charisma score whereas the BoS and the Powder Gangers would have a terrible one.
Perks will be chosen to reflect a faction's talents and skills. Reflecting skills is pretty straightforward (the NCR has good guns skill so they get gun-based perks) whereas reflecting the culture may be different. The White Gloves and the Legion would utilize cannibalism because it can be witnessed within their culture, whereas although the Great Khans may have the science proficiency to unlock Math Wrath, their specialty is in chemistry, and therefore they may or may not get the Math Wrath perk, likely depending on if there are other more-suiting perks available for them. The final level 50 karma perks will be chosen based on how the game treats the faction's karma levels. The NCR would therefore get the good karma perk, the Legion would get the bad karma perk, whereas a group like the BoS or Boomers would unlock the neutral karma perk.
Traits are decided simply by whichever traits reflect the faction best, though of course this is subjective to an extent, but I'm trying to pick ones that are agreeable. Logan's Loophole will be automatically attached to very minor factions, such as the White Glove Society, the Kings and the Powder Gangers. For the moment, (still haven't decided) the Great Khans and the Followers will be treated as major factions and not subject to Logan's Loophole, both because the major factions treat them as one (they seek alliances with them) and because both seem to have more than 15 perks available that would suit them.
Cultural preferences and limitations will apply. The Legion would be restricted from using drugs, whereas the Boomers, when it comes to guns, would basically be restricted to assault carbines, marksman carbines and their unique variants. Why? Because these are the only guns we ever witness the Boomers utilizing. Like Joshua Graham says, each "tribe" has it's own weapons and style, and though a Legionaire may be capable of using a minigun, that doesn't mean they actually DO utilize it. Caesar chooses to equip his Legionaires with other weapons OR they themselves prefer those weapons. This would mean that only the Legion and NCR characters would have access to the mighty Anti-Materiel Rifle and Brush Gun (and unique variants), whereas the BoS is practically the only faction to utilize the YCS/186 Gauss Rifle. Weapons added by the add-ons will be treated as variants of their closest Vanilla NV counterparts, so for instance, the .45 pistols would be treated as 9mm pistols (therefore useable by Powder Gangers and the NCR), the K9000 is treated like a minigun, the Automatic Rifle like a LMG, etc etc. Difficult-to-categorize weapons like the Holorifle....not sure yet. Gotta think on that one, though it would likely be useable for any faction that uses energy rifles (NCR, Legion, BoS, Powder Gangers) or for any faction that specializes in Energy weapons (BoS, FoTA).
This also means that some DLCs will be completed with this in mind. Honest hearts on a Legion playthrough will be....very short, whereas an NCR soldier may kill Dog and Christine in Dead Money; Dog because the NCR doesn't respect super mutants, Christine because she's BoS.
Finally, each character is a pure playthrough. For example, this means the NCR does WHATEVER neccesary to gain NCR rep. The survivors of Vault 34 be damned, the Great Khan drug delivery must be reported to Leutenant Hayes, the BoS may NOT be allied with, Goodsprings WILL be destroyed in order to gain access to the NCRCF and the Powder Ganger quests WILL be completed in order to gain the opportunity to double-cross them for NCR rep, etc etc etc. Companions chosen are also relative to the faction and the culture. Only the Great Khans and Followers seem knowledgeable about Super Mutants enough to tolerate a Super Mutant companion (Lily), some factions may not tolerate a Ghoul companion (BoS, Legion), and other factions may have access to a companion, but no access to a way of completing their quest. (maybe the Powder Gangers could unlock Raul, but would have no way of peacefully talking to the NCR citizens neccesary to complete Raul's quest). I'm also trying to avoid doing things like saying the Kings support the NCR, and therefore may travel with Boone, but rather I'm keeping Boone/Veronica/Arcade/ED-E specific to the factions that are DIRECTLY involved with them. Factions also support whichever faction provides them with the best ending. For example, the Followers may voice doubts about the NCR in-game, but my Followers character would support the NCR because that provides the Followers with their ideal ending, whereas their preferred Indy ending isn't all it's cracked up to be for them.
Having said that, I recently completed my first faction playthrough, having unlocked every item useable by that faction and having reached level 50. Here's my evaluation of the NCR:
http://img.photobucket.com/albums/v174/mr.people/ScreenShot0-1.jpg
http://img.photobucket.com/albums/v174/mr.people/ScreenShot0-1.jpg
SPECIAL
6 Strength (chosen because the NCR utilizes the Minigun and is also proficient enough with weaponry to unlock the Weapon Handling Perk. This combined with the OWB perk effectively gives them a Str of 10 neccesary to utilize all weaponry used by the NCR)
10 Perception (chosen both because of their proficiency with Explosives and because of the stress on their culture revolving around "death from afar" and having good snipers)
6 Endurance (chosen because the NCR Rangers have a unique perk called "Toughness." To unlock the player version of Toughness, one needs five strength. The 6th point comes from the Lonesome Road, placed there simply for it's strategic value (unlocks another implant))
6 Charisma (chosen because the NCR is fairly competent with public relations)
5 Intelligence (chosen because the NCR is neither incredibly bright, nor can they be called stupid)
10 Agility (chosen for their unmatched proficiency with guns)
3 Luck (chosen for their lack of luck on the Strip, and lack of luck with their position in the Mojave
100 Skills
Guns
Explosives
Repair
Merchantile
Speech
Sneak
Lockpick
Science
Medicine
Traits
Trigger Discipline (chosen to reflect the accuracy of their snipers and soldiers)
Built to Destroy (chosen to reflect political commentary that their gear is in disrepair, comments by the Legion that reliance on such breakable gear is unreliable, and to bump up the character's crit rate to reflect that of an NCR sniper, seeing as the 1st Recon Beret provides crit)
Perks
Rapid Reload
Gunslinger
Commando
Sniper
Hobbler
Center of Mass
Grunt
Quick Draw
Cowboy
Shotgun Surgeon
And Stay Back! (both shotgun perks chosen because the NCR caravans are one of the few groups to utilize shotguns)
Hand Loader (chosen because the Gun Runners are "practically a part of the NCR military" and they themselves are capable of producing powerful ammo types)
Finesse (chosen to reflect the crit rate exhibited by the NCR snipers)
Run 'n' Gun
Toughness
Toughness (both ranks of Toughness chosen to reflect the unique perk used by the NCR Ranger Veterans)
Concentrated Fire (the NCR does use energy weapons that require a high enough energy weapons skill to unlock this perk)
Action Boy
Action Boy
Nerves of Steel
Pack Rat
Strong Back (both weight perks chosen to reflect the neccesity of these by NCR caravans)
Weapon Handling
Sneering Imperialist (chosen because the only two major factions this perk increases damage against are the Great Khans and Fiends; the NCR is the only faction to oppose both. And yes, I did use the perk to complete Honest Hearts with a vengeful Graham. )
Thought You Died (chosen because NCR endings heavily imply the NCR is the "good" faction)
Notable weaponry useable by the NCR
Basically every gun. Lucky, ALSID, Gobi Sniper Campaign Rifle, GRA AMR, Medicine Stick, Bozar, K9000, CZ57 Avenger, Survivalist's Rifle, All-American, Hunting Revolver (GRA), Trail Carbines, Cowboy Repeaters, Riot Shotguns, 12.7 mm pistol and variants (Lil' Devil and That Gun), Vance's 9mm SMG, etc etc etc etc.... It should be noted that the way I'm playing the character, it does NOT have access to the Ranger Sequoia or Maria DIRECTLY. The NCR never had knowledge of the Platinum chip AND it's possible to play the NCR without ever confronting Benny, so I did. The Ranger Sequoia is used by the NCR, but in order to obtain one you'd have to kill an NCR veteran or let Hanlon die, both of which gain NCR negative rep or a bad NCR ending, which is taboo by my rules. If I found a way to rob Benny or a Vet with the Sequoia happened to die, however, I could obtain and use them.
Also worth mentioning is I stayed away from Assault Carbines and 12.7mm submachine guns because I never actually witnessed a citizen of the NCR using these two.
Aside from guns....hand grenades, frag mines, Chance's Knife and Blood-nap are a couple weapons utilized by the NCR. I also used Grenade rifles like Thump-Thump for a time, both because the Grunt perk and because the weapon is IMPLIED to be used by the NCR (or you could count Happy Trails as a part of the NCR), but then opted not to simply because no NCR soldiers actually use it in the Mojave.
As for which of those weapons I chose to carry? ALSID, Medicine Stick, Bozar, Survivalist's Rifle, Riot Shotgun and the GRA AMR, though the Bozar and the Survivalist's Rifle were carried mostly because they embodied the NCR, imo. I could survived without the SR and the CZ57 Avenger might be a superior option to the Bozar.
End-game armor
Elite Riot Armor, Elite Riot helmet and 1st Recon beret (yes, both can be equipped. The beret is a hat, the helmet counts as eyewear)
Stats:
HP: 565
DT: 40.4 (this massive number is thanks to two levels of Toughness, the Elite Riot armor and the Sub-dermal implant)
Crit Rate: 21%
Action Points: 125
Carry weight: 280
Potential DPH (as seen in Pip-Boy, Hollow point not being included in this category): 239 (GRA AMR with Explosive rounds and Lonesome Road perk)
Potential DPS (as seen in Pip-Boy, Hollow point not being included in this category): 639 (CZ57 Avenger with custom load rounds and Lonesome Road perk)
Companions available: Boone, Cass, Raul, Rex (peaceful Boone to reflect NCR's regret over Bitter Springs, peaceful Cass to meet the best possible NCR ending quota, Gunslinger Raul to match the fact that the NCR NPCs involved with his quest are fighters, Raul with Rey's brain since the other two options come from enemy factions)
Notable restrictions: Can use Turbo, but doesn't have access to the recipe due to poor relations with the Great Khans
Notable strengths: Has access to every chemical, can knock down enemies with shotguns AND has access to the Riot Shotgun. Can one-shot most enemies with a sniper shot.
Pros:
-Highest possible VATS guns accuracy in the game. VATS is finally useable. With all the accuracy perks, the NCR soldier basically has a free kill button, with VATS typically succeeding 95% of the time. Crouching with the AMR loaded with custom-load ammo, you can get up to 75% accuracy even at the maximum possible VATS range. ALSID is particularly useful in VATS due to it's poor ironsights in free-range shooting, and because you can unload a full clip with one round of Vats. That combined with Concentrated Fire usually means that by the end of the clip, you have 95% accuracy. ALSID also highly benefits from the increased crit rate of VATS.
-Insane Damage Threshold. For having a very modest Endurance, the NCR has a surprisingly high DT.
-Very high HP. Again, for such a modest Endurance, the NCR soldier has very high HP.
-High damage output. The NCR has access to every single damage amplifier available to guns, meaning their overall damage output is exceptional. This is the highest you'll ever hit with a guns character, the only possible improvement being 7% more crit and 100% more crit damage
-Night-vision
-Cannot be crit on.
-Has the diplomatic skills capable to pass on a lot of tough fights
-Access to practically every single end-game gun.
-Very nice Crit rate, only 7% below the highest possible.
-Highest possible perception without ED-E
-Fastest possible reload time
Cons:
-While the free VATS usage is nice, it feels very....limited. A Legion character gains new abilities with their melee and unarmed attacks, whereas an NCR soldier only gains....more accuracy. Even at it's prime, you'd much rather manually aim for the head of that deathclaw at a much greater distance than VATS is capable of, rather than rely on the 75% once the deathclaw is within a distance where a missed VATS shot means you'll have ~2 seconds to react once you leave VATS. VATS is more of a convenience, allowing you to drop all those Viper gang members in 4 second flat, instead of manually chasing them around for 15. The result is that the character has about 15-20 perks that seem lackluster or unneccesary compared to others.
My Overall Grade: A-/B+
While the NCR soldier definitely feels very strong with very high damage and defensive capabilities, it STILL feels like missed potential. Don't get me wrong, it's very strong, but yet I feel it's perks fall far behind the ones obtained by other factions. While the Legion can't be knocked down, runs fast and can kill ANYTHING with a single punch and the Boomers and BoS are dealing outrageous damage with explosives and/or crits, the NCR soldier is busy learning how to master a failed system that only serves as a bonus rather than a lifesaver: VATS. Off of the combat field, it should be noted that the NCR is also very capable of handling issues passively, and it DOES have access to convenience perks like Pack Rat, so it remains very comfortable to play. Overall, while definitely very, VERY strong, convenient and capable, it doesn't quite feel like the STRONGEST....
Next up to review....Legion, Powder Gangers, Boomers, BoS. I'll post info here about my impressions of them once I complete their playthroughs.