As an individual that owns both consoles, there really isn't much of a difference especially if you are comparing the Xbox One version without the Kinect. Early 3rd party games (because how kinect was configured) ran at a lower resolution on the Xbox One (720p/900p vs. 1080p) but not every game runs at 1080p on the PS4 either. Current 3rd party games run at the same resolution on both consoles.
The biggest difference are the exclusive titles. Halo MCC, Ryse, Forza Series, Dead Rising 3, Sunset Overdrive vs. The Last of Us, MLB 14: The Show, Infamous: Second Son, Killzone: Shadowfall.
Other more minor differences are in the controller. The Xbox One controller has rumble triggers along with the standard rumble in the controller and the battery life (play and charge kit) gets about 4 times as much time before recharging compared to the 8 hours you get on the PS4's internal battery. The PS4 also has a light feature (which changes during gameplay) and a small touch pad in the center of the controller which in games that have used it, I have liked it a lot. The battery life on the PS4 is it's biggest downfall.