in terms of gaming performance,
radeon hd 6770 1 gb gddr5 > hd 6670 1 gb gddr5 > hd 6570 1 gb gddr5.
if the card has ddr3, it will perform lower than it's gddr5 counterpart.
2 gb vram is wasted on gfx cards with these gpus, they only add to price and add nothing to performance.
the 6770 (reference design) requires a pcie power connector.
6670 and 6570 (reference design) don't require any pcie power connector.