If you go LGA 2011, you are wasting your money unless you get a six-core i7 and use software that is well-threaded enough to run much faster on the six-core i7s than on the quad-core models. That usually means that you'd have to use software that can effectively use at least ten threads because anything that can use eight or less will run, although faster on the i7-39xx CPUs, probably not faster enough to be worth the expense.
Generally, for gaming, the Ivy i7s on Z77 are better choices (more accurately, it's usually better to go down to an Ivy i5 such as the i5-3570K) because there aren't many situations where they're at a real-world disadvantage to the six-core SB-E CPUs. In fact, the only such situation that I can think of is 120Hz gaming in BF3 MP where an overclocked i7-3770K might simply not be enough to compliment a 120Hz display. Otherwise, gaming would either favor the Ivy CPUs or they'd perform so well that it doesn't matter.
For work where more than four of Intel's cores may be important, then you may have good enough reason to go for an LGA 2011 build, but never with the i7-3820 unless you only got it as a stepping stone to an i7-3930K. The i7-3820 simply can't beat the i7-3770K by much, especially at stock where it often loses (very slightly) and it consumes a lot more power (more than even Sandy Bridge models, undoubtedly thanks to its larger cache, PCIe controller, and memory controllers).