Are you looking for more of an RPG, and you don't really mind if the exploring isn't enjoyable? Then you should get New Vegas. The exploring is really bad and not worth it at all, and can turn you off quickly if you're expecting a world as rewarding to explore as one of Bethesda's. But, it's quests are better, the writing is better, it's far more of an RPG, and it's the game you should play if you're interested in also playing Fallout 1 and 2 at some point. You just need to treat the game as if it's not open world, sticking to the quests because going off and wandering on your own is a total waste of time.
Do you value exploring over just about everything else? If so, buy Fallout 3, it's sandbox is typical Bethesda fare and if you can spend hundreds of hours exploring Oblivion than you can spend just as much time in Fallout 3. The trade-off is that it's not as much of an RPG and has less choices than New Vegas does. Fallout 3 also has a very different atmosphere than New Vegas, and it feels much more post-apocalyptic.
Assuming you played those 1084 hours exploring, then Fallout 3 is the game for you. Fallout 3's replayability comes from exploring, New Vegas' replayability comes from it's quests and the different choices you can make. If you decide to get Fallout 3, you should of course definitely get Fallout GOTY.
I don't know much about mods and if they work well with the Steam version of Fallout 3 (though they work well with New Vegas due to the fact that New Vegas requires Steam anyway), but if you want the game that has the larger about of mods to choose from, get Fallout 3 as it's modding community had a 2 year head start on New Vegas.
I hope I'm wrong, but I have a feeling this is the most non-biased answer you're going to get. I may be biased towards exploration but I can also see why people like New Vegas. Most people here aren't quite as willing to recommend the game they don't like.