Now I know that fanboys will hate me for saying this... but, the Xbox One version seems to have slightly higher image quality. The texture filtering looks better and the aliasing looks less muddied. Again, this could just be the way the videos were compressed and the way they uploaded to the stream. But take a look for yourself. Xbox One is at the top, PS4 is at the bottom.
The rain effects and weather-based reflections from the shaders look about the same on both consoles – based on the footage made available here.
Interestingly enough, the LOD in the Xbox One version seems to extend further into the draw distance than the PS4 version. It looks like you can make out better texture filtering and cleaner draw-distance resolutions than on the PS4.
However, the quality of the light scattering still seems to be of higher quality on PS4. It's probably why in the other leaked PS4 videos taking place during the day time, the game looked pretty good because it handles color correction and light saturation better, where-as the Xbox One seems to perform better at night (potentially because of crushed blacks and the devs making better use of the shaders during the night time?)