If I remember right, ATI changed what there numbers truely represent with the 6xxx series. A 5770 would be something like a mid-mid range, while a 6770 would be a low-mid range in performance. Kinda bothers me they changed what the last few numbers mean in terms of expected performance for a card.
One card is a generation newer, both are a x770, with 1GB of video RAM, yet both are the exact same price, it is due to the 6770 in theory having similar or less performance than a 5770.
The key difference is the 6770 supports OpenGL 4.1 vs. the 5770 support of OpenGL 3.2, among other things that I am not truely aware of, mostly architectural changes with the GPU core. In the end the 6770 is a "better" card, but I would probably look for something with slightly more performance.
Honestly, I would look for a 6790 like this one. http://www.newegg.com/Product/Produc...82E16814102931
(Yes, I am a fan of Sapphire graphics cards.)
EDIT: After looking, a 6770 is just a rebranded 5770 in the end, just a FEW very minor useless changes really. This is all due to the rename of ATI to AMD for the graphics cards.