I prefer New Vegas it feels like a near perfect blend of old and new though FO3 was also pretty fun

Pros

More better Ammo System
Crafting
Better writing in all aspects
A proper city(albit sometimes feels a tad empty)
Multiple Factions with most being non hostile on the map
Multiple endings where one ending can influence another ending.
hardcoe Mode
Continuation of Fo1 and 2
Have enjoyed all DLCs so far


Cons
Not much Exploration (though I can understand why and has to a degree been fixed with DLCs)
Lacks Creative weapon creating(railway rifle etc....), would of loved aswell if they included the idea from Van Buran for science players to continue making Poseidon or other pre war companies tech (would of worked well given the crafting feature)
Hardly see NPCs talk to each other (kinda takes away from the city aspect)
While more of a nitpick I really disliked the assult rifles in the game just looks out of place compared to most other weapons and would of prefered FO3 assult rifles to be in aswell.


FO3

Pros
Great Atmosphere
Some creative towns
Good Exploration
Some really great quest designs
Liberty Prime

Cons
Really weak Writing pretty much all round(Was never a fan of RPGs what allow you to create your own chracter and then shoehorn the player in to a personal story)
There was 2 endings and the DLC kinda when oen ending completly pointless (I liked seeing the purfier work in Broken steel....though that was the only good bit for me)
Alot of towns lacked detail
Lack of greyness (though the pitt was nice)
Mothership Zeta....What were they thinking?

@ Kuddlesworth
@ looloolooigotsomeapples

I found the FONV vaults rather tedious too, and not really rewarding. The vaults in FO3 with the mind-control experiments in them were very interesting imo, and well implemented.

They are both different and both great so play fallout 3 and/or nv but don't nag about it all the time. I like nv better but today I played fallout 3 and liked that too

New Vegas

Pros
Better writing.
Better voice acting.
Better world.
Better atmosphere.
More quests.
More towns.
More things to do in general.
More post apocalyptic sounding score.
The return of Mark Morgans Fallout music.
NPC's with personality .
Improved Gameplay.
Improved animations.
NO THREE DOG.
A return to that original Fallout feeling.
Great DLC.
Crafting.
Different kinds of ammo.
Enemies don't level up with you.
More interesting factions.
No random raider spawns.
No gratuitous dungeon crawling.
More mature then Fallout 3.
Your choices actually matter.
No dumb post ending gameplay like Broken Steel.
The Vault Experiments seem to be going back to Social Experiments rather then Bethesda's messed up actual experiments.

Cons
Invisible walls.
Repeating radio songs.
Boomers (I hate them)
Lack of Easter Eggs and random encounters.
It uses Gamebryo.
Vegas is a little too small.
Mini games (this is an rpg, whats wrong with stat based lock picking or hacking?).
Can get a bit boring at times, mostly during the start of the game.
No Malcolm McDowell.
Raising the level cap, it was fine at 30.

Its not that more people like Fallout 3 than New Vegas, its just the majority of the people that played NV started the series with 3 and the two games have entirely different feels to them. Three is focused more around the atmosphere and exploration aspect of the game while NV revolves around the story, power of choice, that kind of thing. Plus NV had a lot of references to the originals that the people that are new to the series and never played the first two just were never going to get, so that turned a lot of the new fans off right there.