I know this is a crazy thought, but... play both. Seriously. Start with 3, it's definitely got a better intro, and the "immersion" is greater - there are still bugs and other issues, obviously, but it's well worth your time.
NV trades a lot of that immersion in for better gameplay mechanics. More types of weapons, more types of ammo, weapon upgrades that make even melee playstyles quite viable. The problem? It's... pretty silly. The first two Fallouts were also silly, with a lot of tongue-in-cheek comments or just wacky humor thrown in an otherwise serious post-apoc setting. FO3 doesn't have much of that - it takes itself seriously, and so I was able to get drawn into it far deeper. The feeling of wandering a truly desolate wasteland, ravaged by humans and by time, scrounging what you need to survive whilst avoiding any unnecessary conflicts that could easily spell your doom. I loved it.
F:NV has a lot less of that. The map is more crowded, and far more linear. Even early on (especially if you have the full edition with all the dlc items) you have weapons that are competent-or-better, so you can jump right into the exploring and skip as much storyline as you want. Luckily, F:NV does have a setting to retain a LITTLE bit of its immersion: avoiding the wild wasteland perk will remove some of the most immersion-breaking silliness, but a lot of it is still present in how NPCs act and what they say.
That said, they're both "good games." Neither one is "objectively" better than the other - they have different strengths and focuses. The common element that both share is very high quality DLC. Normally I'm not a fan of DLC of any type, and I think it's a fucking cancer on the industry, but Bethesda outdid themselves and made sure that each mini-campaign was worth the time. Sometimes they'll just be small standalone stories, sometimes they'll restrict your weapons and make you go through a FPS training simulator (which mocks the FPS genre as much as possible), sometimes it'll be a massive zone with a shitload of optional content. If you, for some reason, choose not to play both games, rest assured that either one will have some quality DLC content for you to enjoy.
But really, the premise is silly. Play both games; they're the best post-apoc we've seen in awhile that don't go straight for calladoody FPS gameplay.