I prefer 3 for the setting and NV for all game mechanics.
If I had iron sights and the variety of weapons that NV has within the FO3 realm, it would be the perfect game. Which basically means I am absolutely 100% excited for FO4 since that is pretty much what it is going to be. City rubble with massive amounts of customization.
I prefer Vegas by a very large margin. It captured my attention and interest, the story, characters and the writing in general was more convincing and satisfying. There was also more voice diversity and I liked the actors better. I felt way more immersed with Vegas than with F3.
It's not that Fallout 3 is a bad game, it isn't, it's world and ambient is awesome. But in a game, what really captures me is the writing, and Obsidian has/had that done so well with Avellone (who was on Fallout 2!), J.E Sawyer, Gonzales and the other writers.
Sadly Avellone left Obsidian.
First off, applause for the bravery of posing this question. Anywhere else on the internet this would become an all out firestorm. Thank the gods this wonderful site is so civil. I have to agree with Henson that I much prefer Fallout 3's settings, and a majority of Fallout New Vegas' mechanics. I say a majority, because I do feel that some mechanics were a bit over complicated, but that might just be me. There was something about the Capital Wasteland, something about playing from birth to death (pre-Broken Steel at least) of this character that you created, living life in the vault, that first shock of Amata telling you your father was gone. And then that moment. We all know the moment. Stepping out of the vault for the first time. That blinding light in the sky. The desolation like nothing you could have imagined. The people, the places, the history from the old world . . . honestly, I could probably go on for hours about it. For me, Fallout 3 gave me the immersion that I couldn't find in New Vegas. And I know there are people that argue the exact opposite, saying all the same things about New Vegas. Maybe it was just because 3 was my first, who knows, but I can say with no doubt that Fallout 3 is my favorite of the 2.
(Sorry for the long post, I'm new and just getting used to the site.)