5820k has 6 cores (12 threads)
6700k has 4 cores (8 threads)
So for editing, rendering etc the 5820k is faster because of its 50% greater multi-threaded abilities. There are more advantages as games generally will only utilise 4 cores at maximum. So you can use those spare 2 cores for other software while gaming at the same time. Such as I am running a virus scan and playing bf4 at the same time. DX12 should also allow utilisation of all cores but will be a while before it comes into full effect. Some games do like the extra cores.
In terms of gaming clock for clock. There is negligable difference in perfomance between the two.
Both are also very closely priced and both overclock well.
This ^^^^^