The 5820k is on the x99 platform, and it is Intel's HEDT platform for maximum flexibility. Most gamers choose it if they want more than two GPUs (though that is possible with some ultra-high end Skylake boards too), but it can also be used for other expansions as well.
For gaming, you'd certainly be happy with either....but if you have media editing in your normal workflow, the 6 cores and twice the cache is well worth it. Skylake does have some advantages over the Haswell Refresh line, but the Haswell-E negates most of those with it's 28-40 PCIe lanes.
The m.2 slot(s) will burn into your PCIe allocation (both being PCI 3.0 x4), but you have more of them to work with. Skylake runs them through the DMI connection freeing up PCIe lanes, which is important as you only have 16 to work with. Skylake also has USB 3.1 in the mix too, but again, many Haswell-E boards come with that or an add-in card standard.....again eating up PCIe lanes, but you have them to work with (28 in the case of the 5820k).
What it really comes down to is flexibility of the platform, and x99 offers that. Being that you're right on the cusp of purchasing though, I'd consider waiting just a month or so for your purchase decision. Broadwell-E is coming out, and manufacturers have signaled that they will be coming out with new x99 boards to welcome the next HEDT chips. Not that you need one of those boards or the Broadwell-E's (you don't), but prices tend to soften right at that time, and would be great to hit a deal.