New Vegas was a lot more polished. It had better mechanics across the board, but I felt it suffered in other areas for this. It may have had the iron sights and improved companion AI (and don't get me wrong, I loved these features), the story was pretty dire. For all we were promised that there were "no good or bad guys", the NCR are definitely the good guys within the context of the story (while they are more morally grey by our standards), while the Legion were definitely the evil faction.
The story got a little too convoluted for my liking, since a lot of the quests were mutually exclusive; this meant that I either had to read up on the Fallout wiki beforehand to see if I was doing myself out of a later quest or reward, or else just press on ahead and hope for the best. Even then, the story is a bit limp. In one corner, we have the NCR, whose ambitions are to control the Hoover Dam, take over the Mojave and push out the rival factions; in the other corner, we have the Legion who... oh, they want to do exactly the same thing. So do Mr House's robots. How thrilling.
The world in NV seemed a lot smaller too: for all the size of the map screen, a good portion of it is walled off by massive red cliffs. When I tried to go cross-country, I frequently found myself hitting huge invisible walls at the top of rock faces, or else being set upon by over-levelled enemies - neither of these things happened to me in Fallout 3; it's an open-world game, so why are they trying as hard as possible to fence me in?
That said, NV still had a lot more weapons, and the weapon modding feature was a pretty nice touch, but I just don't feel it measures up to F3; Fallout 3 was full of memorable set pieces, had a clear and interesting over-arching story (the same cannot really be said for the glorified series of fetch-quests in F3: Caesar would have me destroy, has an army ready to move, and yet for some reason needs me to go on a public relations crusade for him first), and is just generally fun to play.
tl;dr: Fallout 3 is a fine machine with beautiful components that work well together. New Vegas has a shiny new paint job, but the malfunctioning cogs of poor story and rampant glitches count against it in the long run. Fallout 3 wins IMO.