I own both, the PS4 for a week. I prefer the Xbox One's UI and controller. I also like the voice commands with the Kinect. EA Access on Xbox is pretty good too, it's paid for itself with game discounts already and getting free access to a few games rocks.
Overall, I like the Xbox One better, but there's not a ton of difference between them.
I picked up a PS4 cause my wife wanted to play The Last of Us, and we both want to play video games at the same time.
One cool feature on the PS4 is Share Play, you can share a game with your friends list. I haven't found the light on the PS4 controller too useful, but it's kinda cool that it changes colors with your health in The Last of Us. Plus, the PS4 is the only device I own that lets me stream NHL Gamecenter direct to the TV - I'll be taking advantage of that as soon as the Sabres are good again.
Outside of that, there's not much of a difference between them.
I would buy them based off of which exclusives you like better and what more of your friends have if you play online. IMO that's the real difference between the two.
Sony's customer service is awful. I had to contact them because The Last of Us code was missing from my PS4 Black Friday bundle, and they basically told me too bad, so sad, and they didn't care.
At least Microsoft's customer service is empathetic, even if they don't do anything either.
Sunset Overdrive is pretty awesome. Best exclusive for the Xbox One. I'd call it a great game, but that's just me.