It's really a fictitious piece of market segmentation by Intel for the purposes of creaming more money off people who think of themselves as "high end" users. The so-called "benefits" of LGA2011 are quad channel RAM and higher PCI express bandwidth. But neither of these is of any relevance unless you're running a server with an 8 Core Xeon.
There is one reason (and only one IMHO) to get LGA2011 if you're a home user. That's if you want to get a hex core CPU like the 3830K or 3860X. This is only relevant if you're running workstation style applications (like 3D modelling, simulations and rendering) that require a lot of parallel processing power. Irrelevant for gaming and general use.
So for the vast majority of people, 1155 is the way to go. A couple of points about your proposed CPU choice. First of all, I believe there is little point in getting the non-K 3770. This only has limited overclockability compared with the K version but a broadly similar price. Second point: since it's a gaming build, you probably don't need the i7. The only real benefit of the i7 compared with the i5 is hyperthreading, which is relevant for some applications like video editing, but of no benefit for gaming or productivity. Therefore, I'd recommend you consider the i5 3570K. This is a fair bit cheaper and in games/productivity, has no disadvantage compared with the i7.
(A side note, why do I keep getting the message "sorry this forum is not available?")