Is this is a texture loading issue?
From what I could tell they only shows these issues in the comparison videos during ingame-cutscene and not gameplay. You can tell because the camera perspective on the character and his animation and what transpires.
Usually cinematics preempt the end of one level/area/environment and the beginning of a new one.
Because of the immense amount of texture data that needs to be streamed from the hdd now days some developers are using cinematic as an opportunity to hide load times.
There is nothing that seems particularly more demanding bandwidth wise about rendering that particular cinematic than gameplay where there ARE high res textures on the main character.
The HDD transfer speeds have not kept pace with how much data must be streamed off the hdd. Data that needs to be streamed off is probably at least 4x larger than last gen and more.
Its possible that there were background apps competing for hdd bandwidth with on the eurogamer's ps4, as that is not something the Xbox has to worry so much about as it has the 8GB emmc nand.
And we know its at the beginning of a new level/area and he just got off the jeep and is in the new area and is looking around.
edit: This guy has the hq textures seen in that ingame-cutscene(ps4)
http://www.youtube.com/watch?v=cgUC7DVCOEQ
Also HQ textures in the cutscene (ps4)
http://youtu.be/IEI-szx56zo?t=40m58s
This guy has Lowq textures like eurogamer in that cutscene(ps4)
http://www.youtube.com/watch?v=7badoEqkEHE
Now here is something interesting:
Here is that exact cutscene on a PC or Xbox One with LQ textures (its not specificed but there are A,X,R,L,Y, etc button prompts)
But the ingame-cutscene has LQ textures but high quality in the game
http://www.youtube.com/watch?v=xtztLlVlAEE
edit:2
okay the solution has been found. Its because users are loading their game at the beginning of the level, and the game doesn't load hq textures into memory immediately.
People who play continuously from the end of the previous level have the HQ textures on the main character just like on X1. It looks like this will happen regardless if its PC/X1 or PS4.