A friend of mine brought his XBOX One over to my house a few days ago. I currently only have a PS4 but both he and I wanted to do some comparisons between consoles. I had both consoles hooked up to the same HDMI switch, so both were on the same calibrated input. I also set up both consoles similarly (output resolution, color space, etc.). The following is what I took from the very unscientific tests (and all should only be taken as opinion, not fact):
Call of Duty Ghosts: looked fine on the XBOX One until I switched the PS4 version. By comparison, the XBOX One version looked lower resolution with more jaggies, with the XBOX One's upscaled sharpening method making it look worse than it should. Textures also looked muddy in comparison.
Battlefield 4: looked identical on both platforms, though certain areas on the PS4 had slightly more natural lighting. For reference, I noted that the XBOX One version seemed to have a slightly more contrasty look. Not a deal breaker.
Assassin's Creed IV: PS4 definitely won here. Very little jaggies and everything appeared sharp and crisp, while on the XBOX One there were jaggies aplenty and there was a slight blur to everything.
Those were all we compared, but spent a good hour on each game. Again, that's all my opinion, but