Have you checked your CPU temperatures while gaming? It's possible that it could be throttling.
Also, am I missing something or is your task manager only showing 5 performance graphs for the cores, not 6? Perhaps you'd need to expand the window to see the 6th, it may not be important.
A 6300 will perform decently in BF4. However, most systems will struggle with ARMA 3, it's a very CPU heavy game.
This FPS was with a GTX Titan.