Just for fun, I bought the 360 version of Ep1. (I originally bought it for Xbox One).

They are basically the same, and the visual differences are negligible.

However, the Xbox One version is at a higher resolution and has some higher res textures (ie, Max's shirt). The lighting is different. The Xbox One's lighting feels warmer and more realistic. The frame rate is a little smoother on Xbox One.

The models (polygon counts and facial textures) are identical.

So, for those considering a jump from 360 to Xbox One, there is a difference, but it's the same game.

This is all observation by eye, so if a mod wants to add/correct anything, that would be cool.