It does not really matter for Dolphin since both are powerful CPUs which should be able to run most, if not all games at full speed, especially as they can be overclocked.
The Skylake one does have a little bit stronger single-thread performance (even without overclocking), so if you're mainly going to use the computer for Dolphin, I suggest choosing the i7-6700K. If you're going to multitask a lot or use multi-threaded programs, choose the 5820K since it has two more cores.
Compared to your current i9 930, upgrading to any of the two will be a huge performance improvement, and that's not only for Dolphin.
The Skylake one does have a little bit stronger single-thread performance (even without overclocking), so if you're mainly going to use the computer for Dolphin, I suggest choosing the i7-6700K. If you're going to multitask a lot or use multi-threaded programs, choose the 5820K since it has two more cores.
Compared to your current i9 930, upgrading to any of the two will be a huge performance improvement, and that's not only for Dolphin.