It can handle more intense games and more anti-aliasing. How much of a difference is hard to say... It's 3x the number of pixels, but only 2x the ram, so it better handle the game at 1080p very well with a regular 5850/70 if you want the 4gb version to handle at that res.
ok i was curious. i bought the 2gb version and it runs great on some games and ok on others. I am going to pick up another 5970 2gb and crossfire them... hope it gives me the extra horsepower im looking for.