Always, ALWAYS go for the higher DirectX version, and THEN start narrowing down for performance.
Memory and speed make an incremental difference, but being a version behind in DX support is what will make a game not work, period. Every single time I've needed to replace a graphics card, it's been because it's out of date on DirectX or occasionally Shader Model.
Like others have said, the 5870 is going to be better if you can find it, but a 5770 ought to work fine with anything that comes out in the next 2-3 years. You'll be happy wit hit at least until it's time to get your next CPU.