Any game that runs on the HD8670D will run as well or better on the HD6570.
As it would turn out, the HD8670D, can play almost any game made at pretty smooth frame rates (30-60FPS) at low resolution like 720P. The VISUAL QUALITY in modern titles will have to be sacrificed with low to medium texture and effect settings, and disabled post processing (no AA), but the GPU can play just about any game made at 30FPS or better. (which is usually the cuttoff for what is considered "playable").
http://www.guru3d.com/articles_pages/amd_a10_6800k_review_apu,11.html
http://www.xbitlabs.com/articles/cpu/display/amd-a10-6800k_6.html#sect0
I wouldn't recommend 1080P for the HD6570 regardless, the render output pipeline is too narrow. Doesn't...