Having watched the whole thing in 1080p, honestly the only difference I can tell in this video is the colors. And that works both ways, in some places PS4 colors looked better, in some Xbox One looked better.
As for the real life photo vs. game colors, I think it's not that simple. In real life we see the world "as it actually is" and can easily tell if the colors arnt natural. In game we don't have this. Sure we can go like "well in real life it looks a bit less bright", but I dont think theres an outright contradiction to like a bit more colorful games, especially when shooters the recent years have been just grey and brown while wanting real life pictures to look as natural as possible. But like I said, in some places I found PS4 colors better, in other places Xbox One better.
Judged from this video, I think the only thing that it comes down to are which kinda colors you prefer (and this can probably be changed By TV settings too) and the FPS. The other video showed that PS4 did have a bit of an advantage with FPS, but when we're talking about like 5 FPS difference most of the time, doesn't really make much of a difference in this game.
I even tried to look for jagged edges, but I couldn't really find them on the X1 video as opposed to PS4. With the car scene with those electrical lines in the sky (basically like 1 pixel line in the horizon..) PS4 seemed to do a bit better while on X1 the lines sorta "disappeared" occasionally i guess due to "jaggies".
I can't really deny being a MS ******, but I tried to look at this as objectively as possible and I don't deny PS4s hardware advantage, but I honestly could not see much difference outside colors which isnt a performance thing anyways.