Under most circumstances I'd recommend the 6950 @ 6970 speeds. However, if BF3 is going to be the main game for which you are getting the system, GTX560 Ti 448 or GTX570 in overclocked states are faster than an HD6970. Even without any overclocking, both of those cards are faster.
Once those cards are overclocked (i.e., near GTX580), the 6970 has no chance at all to catch them in BF3.
http://www.bit-tech.net/hardware/graphics/2011/11/29/zotac-geforce-gtx-560-ti-448-cores-review/6
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YMMV, but outside of few cards like HD5850, AMD cards are generally lousy overclockers compared to NV's cards. HD6970 and HD5870 are poor overclockers to begin with. Neither of the 570 or 6970 cards are going to be fast enough to max out BF3 in multiplayer at 1080P to begin with, so perhaps it's a moot point. And if you disable 4x MSAA, the AMD card is going to be pretty much as good while saving you $.