the 7770 is the better of the two cards. the ram at 2gb is enough for gaming, and willl mostly come into play with mods for games, or multiple monitors and resolutions higher than 1920x1080.
with that said, the 7770 isnt powerful enough of a card to really make gaming higher than 1080 or on multiple monitors worth it, and therefore will be a good choice to play on a single monitor and not necessitate going higher on ram.
Thanks for the quick answer! Will I be able to play Battlefield 3 on ultra 1280 × 720 resolution?