I give up! Too many nvidia guys here.
But again: 7870 vs 660?:
Winner is 7870 by about 10-15%, with new catalyst 12.11, 20-25% could be in the range of possible increases. The 660 has a very low vram interface. It not influences casual games , but streaming engines can be affected by this low performing interface.
Bill of material indicates, that the ati cards are currently of much higher quality in the standard layouts, and also in most custom layouts.
The 7850 has no chance against the 660, but equals a 660ti, which was the intention. The 7850 is just a good performer for its price, not more.
Texture flickering or shadow flickering: partly the fault of the game, bit ati often had this problem with the last cards. It is mainly solved to a good amount, bit the speed trees in clod are a problem, which the driver currently not solves sufficiently.
But nevertheless: They know better. So you should go with the mainstream and buy a half video card from nvidia!
Sorry, but that is my opinion. Although I am also Nvidia boy, nvidia got owned this year! People, who do not see this, are not looking enough or do not want to quote, that their investment wasn't that good.