Most games I would say it isn't going to be a large cpu bottleneck, but BF seems to be well threaded and use CPU well. That said the only good info on CPU scaling so far is for BF BC2. Here is a chart I found and let you draw your own conclusions if it would be worth it to upgrade for BF3...IMO probably would help out.
Only amd processors worth considering for you would be x4 955 or x6 1090 IMO (probably x6, but this review didn't include and x6 for comparison). BF BC2 seems to like L3 cache and cores. 955 and 1090 are cheapest black edition x4 and x6 so could be OC to speed of higher models if you want it.