On the other hand, multiplayer side of the game for Xbox One looks so bad that it's something like Minecraft.
Curious to see what the same game looks like on two new, different systems? This video from IGN should help.
Note that these kind of videos are most useful if you run them at 1080p.
Before you go crazy, remember something else: this is one game, one developed by a third-party. So don't go jumping to too many conclusions!
PS: here's our review of the game.
UPDATE - Below is a video from DigitalFoundry that's probably more useful, since it's entirely side-by-side comparison footage.
Battlefield 4: PlayStation 4 vs. Xbox One comparison [DigitalFoundry]