Of course 4770 is better than 4570, but when it comes to gaming 4570 will do the job. Unless you have big budget, then go with 4770k
BF4 CPU benchmark http://static.techspot.com/articles-info/734/bench/CPU_01.png
The difference between i7-4960x (1000$) and FX 4100(110$) is 4 FPS, so it's better to invest in GPU. What GPU do you plan to use?
EDIT : Personally I'd advise you to get i5 4670k