I wound up preferring New Vegas. I REALLY wanted to like Fallout 3, and I gave it a solid 80 hours but ended up dropping it.
I think I found the whole place very bleak and hostile and well....brown. It seemed like everything I ran into was pants-on-head-retarded, wanted to kill me, or both.
New Vegas on the other hand, I felt the world was a bit more alive and colourful, characters had more personality, and I enjoyed the companions/factions more. New Vegas just seemed to suck me in, and once I had the hang of the game, I went exploring and just keep finding more locations.
Of course this is just me and the sort of atmosphere I prefer, anyone who prefers a gloomy sense of isolation in the world, and a darker, bleaker game world would probably plump for Fallout 3. Not to say there weren't plent of things I liked and annoyances in both games mind.
I do wish New Vegas had used a new engine though, and had more radio songs (though the repetition does actually make me turn on the ambient tracks quite a lot, which can be surprisingly lovely, and frankly 3-dog got on my tits).
New Vegas has less sewers/sewer-type areas too. For me they're pretty much like dark dank dungeon caves in fantasy games, not a fan.
Mods don't factor in for me, my laptop can barely handle running at the moment.
As with anything like this though, ymmv