I shoot the 500 5.6 with the D500 and the D850. The D850 is the clear winner in my opinion. The D850 seems to do magical things with the 500 5.6. I find myself using the D850 more and more with the 500 5.6 lens attached.
That said I still like using my Nikon 200-500 on the D500. I have been using the 200-500 since it came out and find it capturing great images. Even at 10 frames a second thanks to the electronic aperture. It delivers rock solid sharp images throughout it's zoom range.
And yes, it is heavier than the 500 5.6 but it is still manageable.
I use both rigs hand held and have had no issues doing so.
I shoot at Wakodahatchee Wetlands and Green Cay on a daily basis and I see lots of folks using mono pods and tripods. But they are limited and cannot react as fast as a hand held system. Not to say that they do not capture beautiful images.