Three key differences:
1) Core counts (1151 max 4 core 8 thread CPUs)
2) PCIe Lanes from CPU, (16 on 1151, up to 40 on 2011 CPUs)
3) Memory controller (dual channel on 1151, max 4 DIMMS, quad channel on 2011 CPUs, max 8 DIMMs or even more with server grade RDIMMs).
If you NEED massive memory capacity (>64GB), or ultra fast RAM, or more than 2 graphics cards, or more than 4 cores, then you have to go 2011. Otherwise you can save a lot of cash by sticking with 1151. Until recently entry level 2011 CPUs (like the 5820K) were actually priced competitively and you could make a solid case for going that platform for a high end gaming PC. Intel's recent Broadwell-E release were a real kick-in-the teeth, prices up across the board, really pushing the platform out of the mainstream market IMHO.
For a gaming machine now, you're almost certainly better sticking with 1151.