I know Nvidia better than AMD, but I can recommend you :
- Nvidia : GTX 770 or 780 (if you have the budget, otherwise 770 will be fine)
- AMD : 7970 or Ghz edition
For AMD, I think the 9000 series are coming soon also so maybe you can wait a bit if you don't want to go for a 770.
I'm pretty sure the fx-4100 will bottleneck pretty bad for a video card with that high of performance, especially in multiplayer BF 3 and 4. He may need to look into a FX-6350/8350 to eliminate some of that bottle neck as well.
I would say you need to upgrade both CPU and GPU honestly. Some games will be fine, and other CPU intensive games may run less than desired. BF 3 single player is more about the GPU, but the multiplayer likes alot of cores to maintain playable framerates.
Regards.