Your experience does indicate a cpu limitation.
Run this test:
Limit your cpu, either by reducing the OC, or, in windows power management, limit the maximum cpu% to something like 70%.
Go to control panel/power options/change plan settings/change advanced power settings/processor power management/maximum processor state/
This will simulate what a lack of cpu power will do.
Conversely what a 30% improvement in core speed might do.
You could also experiment with removing one core. You can do this in the windows msconfig boot advanced options option. set the number of processors to less than you have.
This will tell you how sensitive your games are to the benefits of many cores.
If your FPS drops significantly, it is an indicator that your cpu is the limiting factor, and a cpu upgrade is in order.
The intel haswell cores are some 30% more effective per clock than the FX cores.
What is not known is how well multithreaded YOUR games are. Most like sims, mmo and strategy games are single threaded.
BF4 single player is not particularly cpu intensive. Multiplayer with lots of participants changes that considerably.
4690K with a conservative oc is just about the best gaming cpu available today.
Your budget might buy the cpu, but you will need a Z97 based motherboard to go along with it.