Not much unless you are playing on really high resolutions or you are using Anti aliasing. Normally its not worth it to get the 2gb version. Instead, its better to just get a faster card. What card are you inquiring about.
depends on your gaming resolution, the games you play and the rest of the hardware in your box. IMO if you game at 1600 resolution or higher get a 2gig card........ unless you are talking about the 550 or 7770 area where it wouldn't matter because the cards don't perform at high res very well.