F:NV has like three more times quests!
(but I know F3 has more dungeons)
If you want the more “Fallout”-y experience, New Vegas.
If you want “Oblivion with guns”, F3.
Personally, I liked F3. I LOVED New Vegas.
Fallout 3 GOTY Edition.
I much preferred Fallout 3 to New Vegas; I found the world much more vibrant and alive with things to discover. New Vegas felt too… cramped. They included big set pieces every so often in an effort to create places of interest but the open environment of Fallout 3 created a much more interesting and immersive experience, I felt. In Fallout 3, you could wander for hours on end and find only one or two big set pieces, but countless numbers of little things. I picked it up after a full year and resumed my save game, only to discover that there were so many other things I still hadn’t discovered yet. New Vegas didn’t have that same level of exploration.
So yes, I reiterated what everyone else just said. More linear, go with New Vegas; open-world, go with Fallout 3. (Though, for the record, I enjoyed the DLC for Fallout 3 more as well.)