The main questline in NV is to go to Vegas and find the guy that shot you in the intro, it unfolds from there.
What I did not like about F3 story was that it was too linear. Don't want to go into that too much as I don't wanna spoil anything for anyone. NV just gave the player way more freedom when it comes to how the story plays out. There are multiple different factions you can join which completely changes the outcome of the game. You can also do the "selfish" thing and finish the game with only your own interesest at heart.
The overall writing in NV is also just way, way better than in F3. This is, obviously, because Obsidian's writers are leagues ahead of Bethesda's. I mean these are some of the guys that made/wrote the original Fallout games, Icewind Dale, Baldur's Gate, Planescape Torment etc. back in their Black Isle days. Bethesda is known for Elder Scrolls and F3, neither of which are known primarily for their storytelling.
IMO Bethesda knows how to make a good open world game based on exploration, not roleplaying. It's a lot better in F4 than it was in F3 though.