performance should be exactly the same with either cpu. BF3 and most FPS games dont tax the cpu much so i dont expect BF4 will either. The 4770k is a very capable cpu so have no worries.
The 4770K is the better choice for gaming the reason to go LGA 2011 apart from 6 core CPU's is extra PCIe lanes if you need them with a quad like the 4820K.
+1 for the Intel Core i7-4770K http://amzn.to/14A0Bvq for Crossfired AMD Radeon R9 280X's http://amzn.to/19PQa74 The 4820K would be needless for gaming. The 4770K will be plenty for what you want.