New Vegas isn't a sequel, per se; it's a new story set in a new place with new characters in the same game engine. New Vegas has a few additional features -- most notably "hardcore mode," which requires you to eat, sleep, and drink water -- but the essential game mechanics are identical. So I'd suggest that if you're not interested in playing both, choose the one whose setting you prefer (probably the real-world city you've visited the most) and play that. You're not going to miss any plot points by skipping FO3 because the player-characters are totally different.
However, if you plan to eventually play both games, I'd suggest doing FO3 first simply because I've found that when you go back to FO3 after playing FNV, FO3 feels a little stripped-down without the additional features. (I get so frustrated at not being able to aim down the sights in FO3 now).
But if your gametime is limited, there's no need to play both unless you're a die-hard post-apocalyptia fic fan. There's at LEAST 60 hours of gameplay for a first-timer, and that's if you don't do too many of the side quests. I put 95 hours into my first playthrough and I didn't even visit all the locations on the map. I fully intend to go back to a previous save and put another 15 - 20 hours into my first character before I start my second playthrough. And New Vegas is very amenable to multiple playthroughs -- it's simply not possible to do everything there is to do in a single go. (Some of the choices you make close off other paths.)
So if you're just wanting to find out what all the fuss is about, New Vegas will do that for you just fine. You know where to come if you get stuck.