Though I prefer New Vegas myself, I think it comes down to what kind of game you're looking for, between the two of them. I think that Fallout 3 was designed as an open world game from the ground up; this meaning that the story is only served to cause us to explore the world they made; and I will admit that Bethesda created a brilliant, yet depressing world to explore. This is to contrast New Vegas which I believe was designed from a narrative point of view, wherin the exploration compliments the story thus meaning the locations were designed to create the stronger narrative. While New Vegas's world is still varied and interesting it doesn't have the same punch FO3's did, the story was much stronger, while losing in exploration while Fallout 3 made up for the weaker narrative with excellent exploration. Two different types of games.
There's also the smaller factor of which would play better into the originals if you're more of the older fan of Fallout, which in that case, New Vegas retains much of the earlier works' canon, such as the NCR, The Brotherhood being less of saints and more of hoarding assholes and in general that feel is much stronger than in Fallout 3's isoloated DC area.
Basically if you liked the great exploration of Fallout you'll be disappointed in New Vegas whereas if you, like me, were disappointed by the less than stellar story of FO3, you'll find comfort in New Vegas's tighter, more coherant narrative. That and at the start you needed to be very tolerant of bugs, another throwback to the original saga.
