The Xbox One game has clear disadvantages against the PlayStation 4 release that we'll explore in a moment, but they're best described as annoyances as opposed to anything genuinely game-breaking.
Beenox has at least handed in a native 1080p presentation on both Xbox One and PS4, as promised. This is backed up by what appears to be standard post-processing anti-aliasing, seemingly identical between the two games.
The most immediately noticeable difference between the two platforms is the gamma level - it seems to be excessively skewed on Xbox One, resulting in clear black crush, especially impactful in night-time scenes, where PS4 resolves detail in a much more agreeable manner. Other differences are thin on the ground - there are some examples of textures shunted across and warped where they shouldn't be on Xbox One, and we also see a heavier/blurrier depth-of-field implementation, but these things aren't very noticeable and don't impact on the enjoyment of the game
While 1080p30 is the target, the PS4 release does the best job of sustaining that performance level. There are a few dropped frames, but virtually nothing impedes the flow of the gameplay. It's a different story on Xbox One, where we see the implementation of an adaptive v-sync - the game caps frame-rate at 30fps just like the PS4 version, but unlike the Sony platform, frame render time often slips over budget. At this point, the game flips the framebuffer as soon as the next image is ready, while the console scans out to the display, causing screen-tear.
On top of the crushed colour range, it's the tearing that's the key factor of differentiation between the Xbox One and PS4 versions of the game. It's a little annoying, manifesting mostly as a distracting wobble on-screen, making the experience less solid than the same title running on the Sony console.