When getting into this level of gear you need to also be looking at the whole environment, what lenses are available, what accessories are present and all these things. At present I'm heavily invested in Canon glass so I'll be staying with Canon for the future.
For you going from a 600D to either a Canon 5D4 or D850 would be a huge step up. But making sure you can use the lenses you want and all that I think is the bigger question here, its more of what system do you want, rather than camera at this point.
I want a D850, but havent handled one yet, though in a couple of weeks I'll probably get a chance.
The D850 was released to celebrate that Nikon turned 100. For all I know, its an exceptional camera. It beats the 5D4 in most areas. Namely it has the best sensor on the market, while Canon has the worst. It also has very good build quality, basically on the same level as Nikons one digit cameras. It has the best viewfinder of any Nikon DSLR. Despite the high resolution of the sensor, it can reach fps that are good enough for professional sports (7fps regular, but 9fps with battery grip and the large Nikon D5 battery). For what it is, its dirt cheap, too. The battery grip and D5 battery plus D5 battery charger is extremely expensive though.
It is however NOT silent. The D850 is all metal inside and the regular shutter is really loud. The predecessor D810 has a lot of plastic instead and is very silent. The D850 has a silent shutter in lifeview mode, but then it has all the usual problems - rolling shutter, cant use flash, stripes if theres artificial light, etc.
Cant say about ergos, I'm used to Nikon and cant compare to Canon. Though the D850 uses the new element placement first tried on the D500, people seem to love that one.
The 5D4 is definitely better for video, since Nikon has nothing but regular contrast autofocus for lifeview mode. At least they FINALLY added focus peaking - though ironically it doesnt work with 4K video, which is just absurd.
I think the image-comparison at dpreview is very helpful. They both seem to have a similar modus in replicating colours and edges, the 5D mark IV is nothing like its predecessors in that respect. Other than that I think it mostly comes down to what lenses and ergonomics you prefer, I don't really like the Nikon-grip, but that's subjective.