Your heavy hitters would be the Brotherhood and possibly the Enclave. Their units would be the most expensive to train, not very diverse, as it would effectivly be powered armored soldiers just with different guns for different situations, and they would have a low population limit. The upside is that thier units are very powerful and even their specialist units can handle a variety of situations. The Enclave campaign would have you begin to go to certain Vaults to bring up your population, securing weapons depots and bunkers and eventually culminating in a restoration of the Enclave. The Brotherhood Campaign would be the D.C. Brotherhood pushing back west to unite the Brotherhood, either by force or diplomacy (AKA kill these guys and you have our laser rifles) eventually butting heads with Caesar's Legion and the NCR. You would make decisions as a general and your commander (basicly the hero) would do them and give their imput, the Enclave commander (basicly a powerful hero unit) would frown upon showing mercy and is completely ruthless when it comes to the Enclave's goals all with that patriotic gung-ho attitude that a cetain sergeant in Fallout 2 had. The Sentinal that would be the commander under your control for the Brotherhood is more merciful, but will also insist upon executing what he/she believes to be dangerous individuals. These choices determine how much good your faction does or how much damage it causes.
On the other end of the spectrum we have the swarm that is NCR and Caesar's Legion. They would have a high population limit, cheap quick to build units and are more manuverible compared to their power armored counterparts. The downside is that their units require a swarm to take on strong foes and the specialists are appropiatly named because they are a master at only one thing, and Rangers and Power Armored Shock Troops are still not as powerful as what the BOS and Enclave have. This could focus on a joint campaign, where after the events of Fallout New Vegas the NCR pushes into Arizona, forcing the Legion to be on the defensive and making the NCR invaders. Eventually it would end in a stalemate and set the scene for another Fallout game. As the Legion you will wage a bloody guerilla conflict with the NCR, trying to hold them back as long as possible for time to regroup (3 out of 4 endings end with the Legion getting it's ass kicked) and make a stand. Like the Enclave, the Legion commander under you is a ruthless individual, but also a sadist who wants to crucify and torture anything in the name of Caesar. For the NCR you are trying to push deeper and deeper into the Legion's territory, you also need to find a way to survive and defend in case of Legion counter attack to wait for your reinforcments in the other half of the campaign (which is basicly after the Legion regroups and stops your advance). Your Veteran Ranger is a cold bastard who would kill every last Legionare with his bare hands if he could, but can also see the big picture of your choices and will call your out for being irrational or taking to soft a stance with the Legion. Again your choices will effect how the people of Arizona view your faction, will they be appalled at how brutal the Legion becomes when on the defensive or understand their actions? Will the people see the NCR as liberators or invaders no better than a raider tribe.
Naturally you would have some powers to go along with these factions. Enclave will get to use missles and other high tech WMD's, Brotherhood would get to use a cheaper version of Liberty Prime, NCR can call in artillery strikes if they build the cannons and the Legion can get swarms of mongrels (may not sound powerful but if a dog reaches anything without Power Armor that person goes down in one shot) that are easy to kill but pack a punch.
So what do you think? Any ideas or suggestions would be nice I only had 30 minutes to type this up.