My Setup:

MOBO: GA990FXA-UD7 

CPU: FX8150 @ 4GHz

RAM: Dominator 16GB DDR3 1600 

GFX Card: 2 Matrix 5870p's, Crossfire @ 930MHz

GFX RAM: 4GB GDDR5 @ 1250MHz

PSU: Corsair AX1200

To fix the issues in Crysis 3, I found that using RadeonPRO BETA 1.1.1.0:

http://www.radeonpro.info/en-US/Blog/7580576579578485512/RadeonPro-Technology-Preview-updated

With SMAASweetFX Injector:

http://forums.guru3d.com/showthread.php?t=368880

Fixes the issues for me. Use RadeonPRO to control the graphics settings and SMAA SweetFX. Do not force Vsync with the program. For me that caused Vsync to not work in Crysis 3. And do not use RadeonPro's overdrive. In Crysis 3 it causes problems. Just stick to the CCC Overdrive. 

Also, there is a configurator that was made by one of cryteks R&D engineering people. It is awesome. Works like a charm.

Found here: http://secure.mycrysis.com/forums/viewtopic.php?f=65&t=56955

In using these programs, I have made the game look absolutely beautiful and all the while keeping a steady 60 fps. Runs very smooth, for having everything cranked way above the in game 'Very High' setting. Hope this works.