New Vegas. Hands down.
Far better writing (IMO, thanks to Obsidian) weapon mods, iron sights, better melee weapons, better companion system, cooler factions etc.
I'm actually playing NV as I type this.
Fallout 3 is by no means a bad game, it is amazing but NV improves on it an almost every conceivable way. I'm not the biggest fan of the forced character backstory in F3 (although it was awesome the first time). In NV it's mostly left up to the player.
Both games also have a crapload of mods to make them play/look better.
Edit: [MENTION=193]matt[/MENTION]. Whichever game you choose, rather try for PC if you can. If you have to go the console route get it on X360. Lots of issues with both games on PS3: stuttering, freezing etc.