Anandtech.com has a handy benchmark comparison tool
that will answer all your questions (although not specifically for BF3). I've queued up an i5-2500K for comparison which is really at the optimal price/performance for enthusiast gaming machines. Going for an i7 is really only necessary for power users with a specific focus that requires 8 threads or people with deep pockets that can't figure out where else to spend their money. The good thing is that BF3 is more of a GPU limited game, whereas games that reviewers use to compare processor gaming performance
are always CPU limited for obvious reasons, they show the largest FPS delta between different processors. TR also did an article regarding BF3 performance of a few GPUs
of which your 560Ti is one of them....it's worth a read.
Main: i5-3570K, ASRock Z77 Pro4-M, MSI RX480 8G, 500GB Crucial BX100, 2 TB Samsung EcoGreen F4, 16GB 1600MHz G.Skill @1.25V, EVGA 550-G2, Silverstone PS07B
HTPC: A8-5600K, MSI FM2-A75IA-E53, 4TB Seagate SSHD, 8GB 1866MHz G.Skill, Crosley D-25 Case Mod