What is the difference between ati radeon hd 5770 1024mb and 2 gb ati hd5570

the 5770 is better by a lot

The extra memory will help mostly in higher resolution play. The hd 5770 is a faster card.

What resolution do you use, and what is your cpu?

+1 on the 5770 unless your doing photo editing on 3 huge resolution screens or something. 2gb is a waste in any 3d application with a card as weak as a 5570 because the card will never be able to handle a resolution high enough to need the extra vram.

^+3
If you are a gamer then absolutely get HD5770, it's much faster than HD5570.