The 6970 has 2GB vram which is way overkill for 1080p.
Also the 570 has excellent driver support.
Both cards are on par, get the cheaper.
and one more thing, Dont get the FX8 core, you're better off getting a FM1 A8 CPU for gaming as the power consumption is lower and the CPU is more efficient.
Consider a Intel Core i5-2400 system if you're willing to dump the cash for a FX8core
Ignore the comment.
The Sandybridge i5 2500k is what you should be looking to use as a gaming platform.
The i7 is not a gaming cpu unless you want to render and encode all the time.
The i5 2500k is a beast and walks all over all i7's from last generation.
Technically the A8 CPUs aren't suppose to outperform the FX8 cores, nor are they able to at their stock clocks, but they are by far more efficient,
since the FX8cores cant even beat the old Phenom IIs, I suspect a A8 APU clocked similarly to a FX8core can beat it quite a few applications as the A8s are based on the old Phenom II architecure.
and Get the i5-2500K, it overclocks fairly well.
http://static.techspot.com/articles-info/452/bench/Gaming_01.png
http://static.techspot.com/articles-info/452/bench/Gaming_04.png
What reasons other than bragging rights?