I loved the game. I found it to be better in every way compared to Fallout 3 with the exception of interior level design. Seriously, every time I entered a building I was scared of getting lost in these labyrinths and being eaten by a minotaur.
The Mojave was more interesting and lively then the Wasteland. The story wasn't bathed in stupid(and I don't care if story isn't the point of a Bethesda game. If that were the case, why do they put one in?) and that you had a pretty big influence on. It continues some story's that were in Fallout 3, fixes the gameplay so you don't need to rely on VATS, and finally made 3rd person a viable gameplay choice. The characters were more interesting, the companions were FAR more interesting, and easier to manage. The world wasn't so grey and bleak(although so much orange does get annoying). They did away with morality and instead used factions, which is a brilliant move. No longer are you tied to a stupid morality meter, but have to instead choose based on how your choices will affect other people. And the people actually comment on the changes to the wasteland. This makes it feel like a live place, a changing place. In Fallout 3, you could blow up Megaton, and only your dad and 3 Dog would notice it. In New Vegas, when you do stuff, people notice. Its DLC seems to be adding a whole new story-arch, which seems like it'll culminate in an epic showdown, rather then just add a bunch of random crap like Fallout 3's DLC did. New Vegas's DLC items are also balanced to fit into New Vegas, unlike the Fallout 3's DLC weapons and items which break the game.
It was just better for me. It took the old-school Fallout story and world, and re-tooled the gameplay of Fallout 3 to make one hell of a great game.
From all the arguments I see about these games, it seems that those who like Fallout 3 prefer exploration to story, whereas people who like New Vegas prefer a more story-driven experience, and remember the old Fallout games.
Fallout 3 was a good game, but it was a shitty Fallout game. New Vegas is a great Fallout game, and a good game.
Thats my take on it. When I got New Vegas, I immediately un-installed Fallout 3 and never looked back.