I have a P775DM1-G, I have left Furmark running with a mild overclock (+50, giving 1227 core clock) and no issues whatsoever. I had the Intel XTU Burn Test running at the same time. The 6700K got too hot and throttled, but I suspect that was due to running it at 4.5Ghz. No issues with the GPU, nor shutdowns.
I think even the P870DM may struggle to cool a normal 6700K at full pelt.
I have been playing Tomb Raider on the P775DM1-G, at a higher detail than my old desktop PC, and it runs smoothly with the fans "relatively" quietly.
Having owned the P775DM1-G for a couple of months now, I don't see any personal benefit that I could have gained by paying extra for a larger chassis and better cooling in the P870DM. The cost saving paid for a NVME 950 Pro... If money is no object go for the more expensive one. I'm happily playing games without feeling like I've missed out on anything.
It works out the box. I've never had SLI and don't want to have to worry about SLI profiles or whether a game supports it, the 980 just works. The CPU throttles a bit due to current limit throttling...