I have a similar problem with Battlefield 3. In BF3, no matter what I do, the framerate will be in the 15-40fps range. 60fps only if I look into the sky. If I have everything at low and at 640x480, I can't get a stable 60fps going.
I have the same problem with BF4. Am I CPU bound? I have a A4-5300, which I found out has no L3 cache and only 1mb of L2 cache. I have 4gb of system memory and a Geforce 650 GTX. Am I just bottle-necked?
UPDATE Just as a follow up, I went from the dual core AMD, to a "quad" core AMD. The quotations marks are there because AMD is a little shady about what they mean with cores. The quad core AMD performed much better and BF3 and 4 became playable, but the FPS still struggled more than I thought it would, but it was playable. I recently said screw it, bought a i7 4790k Devil's Canyon CPU and now things are perfect. I still have a modest Radeon 270 2gb, but the performance is excellent on all high. BF3 and 4 just demand a solid CPU, mine is overkill now, but you must have a true quad core!