A lot of people committed on the COD review comparison of the ps4 version Xbox one. They saw what I saw in the early days of the ps4 before deep color options were added. They saw haze and washed out blacks compared to the Xbox one. Now this is something that has plagued Playstation for years. It was the driving force behind me keeping a Xbox one as my primary system for games because all my sport titles looked better. However ever since the deep color option and full RGB was used in my pictures setting together all advantages that were there for the Xbox one disappeared. Along with the point of having two systems. Below is a video taken off my ps4 in 720p, not even in 1080p and you can clearly see the difference. Then I notice that the brightness levels were too high in COD which could explain a lot of the washed out blacks compared to the Xbox one, so I lowered that too. Keep in mind what you are seeing is worse looking than the images and pictures off my TV at 1080p, but I think you will see the difference regardless. By the way, I took the other pictures from the feeds off of other players that posted their Xbox one scenes and ps4 scenes in full 1080p.
Ps4 default in game brightness levels. (1080p recorded)
My ps4 brightness levels changes(720p recorded)
Xbox one default brightness levels(1080p recorded)
Even at 720p recording you can clearly see more details in the face and clothing of the characters. Imagine what it truly looks likes in 1080p. So before everyone throws a fit over the results and wonder why the graphics don’t match, this could explain it. Hope this helps.
Just for fun: Here is what another person posted for the ps4 version(720p picture taken with bad brightness settings)