The 5820K is a six core CPU while the 6700K is a quad core CPU. They have similar performance per clock, but the 5820K has a lower stock frequency, so it has slightly lower performance per core. This makes the 6700K better for gaming, unless you overclock in which case the two are roughly equal in most games while the 5820K pulls ahead in games that can use more cores. With overclocking, both CPUs typically reach similar maximum stable frequencies at between 4.5GHz and 4.8GHz. Skylake's minor architectural improvements are somewhat offset by the 5820K's slightly larger cache and wider memory controller, but these are minor differences either way.
The 5820K is so close in price to the 6700K (often cheaper, granted the X99 motherboards are more expensive to compensate) that it makes sense to basically get two more cores for the same amount of money with little to no drawbacks if you overclock. If you don't overclock, then the 6700K is generally a little better for gaming.