at bf3 even at low preset the 7660d plays it at around 20 fps max http://www.tomshardware.com/reviews/trinity-gaming-perf...
So in the end the 7770+phenom wins as i current play bf3 @ high settings at 1080p with a 6770 so that setup should be great and i get about 30-40 fps matters on the map which to me is just smooth enough to be playable but i used the custom settings with mostly high and some medium to get around 50 fps
The 7770 is a good card, people will tell you that its low end (which it is) but it's not as useless as they make it seem. Unless your a real hardcore gamer or computer builder, chances are you'll be just fine with it (I'm super happy with my 7770). For battlefield 3 I don't play but my friend with at similiar setup to mine does. He actually runs a 6770 with a 945 Phenom and it runs on high in multiplayer, but he'll usually turn in down to medium, I guess so he doesn't ever have to worry about his fps dropping, he's a weird guy.
As for what CPU to run with one, I use a Phenom 945, which obviously is lower on the chart than the Phenom 965 you linked, but I'm not sure how they stack up to the A-10. Either way my 945 matches very well with my GPU, usually they'll both stay around the same usage percentage, in some other cases the CPU will be running hard and slowing down the GPU and in other games/cases it's the other way around.
well matters how much dough lol id go with the 7770 and spend more as its newer and overall better, and the website u used for the 7770 only has a 6770 for like $13 less lol
Newegg has the 7770 for $110-120 with a free game and the 6770 for lowest at $100