Can I play hard core game like crysis 3,battlefield3,medal of honor warfighter on core 2 extreme qx6850 with high setting?
As a CPU the Extreme is better. But depending on your graphics card, you should set the game settings. The CPU doesn't play a big role in graphics when it doesn't limit the Graphics card.
So, what is your graphics card?
Crysis3/Battlefield 3 are also demanding games. I would recommend at least a GTX660 if you want to play on high settings or a Radeon HD 7850/7870