CPU should be a decent boost but I am by no means an expert on Intel. If I remember right the E6600 overclocks well too.
The minimum specs for battlefield 3 is a core 2 duo 2.4GHz so it should run. that being said BF3 is a heavy hitter and if you just replaced the board and are doing the CPU too you may have been better off getting a more modern socket/CPU. not sure what you paid for the board.
I believe at your res you'd be ok with a 6770 at medium, maybe medium-high. check the 5770 results here.