Hello,
I used to have a d750 + d500, but sold both and now have only a d850. I use it with the Tamron 150-600 G2 and the Nikon 500mm f/5.6 PF for birds. I also use the battery grip (vello 3rd party) w/ the EN-EL18c (D5) battery to get 9 FPS.
I like the image quality of the d850 better than the d500. It also crops better, I think, even if cropping below the DX size. I almost always shoot in FX mode -- the in camera crop to DX only saves you file size. I also shoot raw not jpeg, as I find that gives me better crops. The dynamic range is a little better with the d850.
Having the FX viewfinder makes it easier for me to find subjects and track them than with a cropped DX viewfinder.
Without the battery grip, the native 7 FPS is a big drop from the d500 10fps. For action and BIF, I would not use the d850 without the EN-EL18c battery. The Vello 2nd gen grip for the d850 works great and is much less expensive than the Nikon original. But you need the 2nd gen to get the 9 fps, not the 1st gen.
I shoot other things besides birds and for that I like a full frame camera for the better DoF blurring. If I was only shooting action or birds, I'd probably stick with the d500. Compared to the d850 + grip, the d500 is much more compact and lightweight.
I do knot know which has the better AF. The d850's AF is constrained to the center a bit more than the d500, but I find both very good and fast.
I do not think there's a significant ISO performance difference between them. It's not like going a lower MP FX like the d750 or a d4 or d5 or Z6. I can shoot the d850 at pretty high ISO, maybe 3200 - 6400, and crop quite a bit in raw and get good results using apps like Denoise AI.
If you have enough light or are using flash, the native ISO 64 of the d850 is beautiful. It works well for product shots, and macro shots with off-camera flash, among other things.
So, to summarize, I wanted to consolidate a d750 + d500 into a single d850, and that has worked out for me. But for action/sports/BIF, the d850 needs the 9FPS battery grip to stay competitive with the d500. If I did not want FX for other types of shooting (portrait, wide angle, landscape), I would have stuck with just a d500.
Marc