Fallout 3 by a landslide for me.
New Vegas just doesn't feel right to me. It's too populated, too urban, too civilized. In Fallout 3 the major settlements looked like safe havens in the middle of a deadly wasteland. Of the two largest towns, one was protected by a massive wall of metal, and the other was an aircraft carrier. In New Vegas, towns are sort of just there, like the Wasteland isn't really a big deal.
In FO3, the centerpiece were the ruins of Washington city. There, the gameplay changed, it was a different environment, a more lethal one. Less room to run and hide, every turn could lead you to a dead end, enemies were bigger and meaner. On the other hand, the centerpiece of NV is the Strip, which is basically a big town with tacky lights.
New Vegas is full of people, of NCR soldiers, military camps, the Strip is surrounded for miles with civilization, suburbs, towns, fields. There is irrigation, a monorail, readily available electricity. It just doesn't feel like a post-apocalyptic wasteland. It feels like a run down town somewhere in Nevada.
And then there are the landmarks. I'm not american, but still FO3 was full of interesting places to visit. NV... not so much. One of the cool things about FO3 was visiting actual real-world places and areas. They made the made-up stuff seem more believable. In NV there's far less of that.
I dislike the fact that NV feels more linear. There is a distinct direction you're supposed to take through the game and the placement of impassable barriers and unbeatable monsters hearded you in the "correct" direction (south, around to Novac, then north to the Strip). As a result, the world feels smaller. In contrast, FO3 doesn't give a fuck where you go after exiting the Vault. Sure, there are a few areas that kick your arse early on, but they are individual areas and can be easily avoided. There's just more freedom.
Finally, there's the western theme. I left this for last since it's extremely subjective, but I just don't care for it. It ruins the theme for me.
New Vegas has more guns and some nice extra mechanics, but it doesn't come close to FO3 when it comes to the game world, atmosphere and such. As a result, I'd rather play FO3 some more.