Quoted from RVH:I don’t think the ps4 pro is actually playing games in 4K.
The new Xbox one X will.
Neither of them support all the games at native 4K. The One X comes close, and on some simpler titles, it can natively render games at 4K, but most titles are still upscaled from a sub 4K resolution using a checkerboard rendering technique. I know a lot of titles these days use dynamic resolution scaling techniques to keep framerates stable.
If you're looking for a monitor that's being specifically used for the best gaming experience, try to find one with the least amount of image processing (to keep latency down), and the highest refresh rates.