Fallout 3 has some advantages. While its save games on the PC were horribly optimized, it was generally less buggy. Obsidian is famous for buggy games and New Vegas was no exception. I feel that it had a pretty tight, coherent narrative. While the followers in Fallout 3 weren't as iconic as Boone or Raul, I still really enjoyed my time with Fawkes. I also felt that it was much easier to explore all of Fallout 3: I played a complete good and an incomplete evil run in New Vegas, and I still barely scratched the surface of the options. I have more nostalgia for Fallout 3.
But New Vegas is still the superior game. The introduction is more brisk. We have a much better reason to find Bennie than we ever did to find our Dad, Liam Neeson aside. The game is a masterpiece of an appropriate placement on a world map of challenges. The game clearly gives you a strong reason to go the long way to Vegas, but if you're a competent player, you can make a beeline to the city and succeed. The follower mechanics are much more robust. While the main arc to me has some issues, it still gives you interesting choices. I feel that the rivalries between the NCR, House, and the other factions are actually not terribly well-explained or logical, but I admire that they tried to paint each faction in shades of gray and give you some interesting choices to try to figure out. They improved a lot of balance issues: V.A.T.S. is more of a strategic tradeoff than an easy mode, for example.