Overall, I've noticed a few key graphical differences between the XO and the PS4 based on what those youtube videos show. Some of these could differ when looked at face to face, but most of the things remain the same irrespective of the quality of the youtube video.
XO relies a lot more on global illumination than the PS4
The colour space of the XO and the PS4 seem to be slightly different, based on the fact that the Xbox has higher colour saturation (this could be a result of HDMI colour correction and gamma differences)
Polycount between the two is same in all games I've seen.
Texture filtering seems to be all over the place, with some games doing better on PS4, others on Xbox
Texture quality seems to be equal or slightly better on PS4. So does antialiasing, although the AA method seems to make the textures more fuzzy on the PS4. This means that the Xbox textures actually appear more defined than the PS4 ones.
Shadows appear slightly softer on the PS4 vs the Xbox (this could be a D3D/OGL difference)
Water reflections seem to be equal or slightly better on the PS4 depending on the game. In AC4 the D3D render path treats water like a mirror at certain angles, while the PS4 OGL render path more accurately takes into account smaller movements.
PS4 seems to have a slightly higher draw distance depending on the game.
Also, Battlefield 4 seems to have a poor framerate on both consoles. Can anyone confirm this?