http://www.guru3d.com/article/msi-ge...hawk-review/18
28 -> 42 fps when swapping 5770 (exactly same performance as 6770) to 560. Hardly 2-5 don't you think? That goes from relatively choppy to playable. There's nothing perfectly good and capable about 6770 unless you're playing old games with low res.
That said, there's no way 6770 is going to run BF3 with proper settings and full HD resolution too well. Probably will be playable if you're prepared to reduce the settings quite a bit, each to its own I guess.