Hi! Welcome to the forums.
First, drop to the normal i3-2100. the xx20 just adds hD3000 onboard video which you won't need since you have the 6870.
-An i3-2100 is more than capable of playing battlefield 3. Don't worry about it.
Could you list the parts you're thinking about? Might help me figure out what you need.
The 2120 is clocked higher too
Its the 2105 thats the same as the 2100 but extra graphics