Owning both, I've found that the technical merits are mostly smoke and mirrors....with the caveat that a few games do run better on the PS4 than the Xbox One, and I tested this out on at least one title (Shadows of Mordor) and noticed that while it plays fine on the X1 it's performance on the PS4 was noticeably smoother.
Beyond that.....Xbox One's two main advantages I've found are: you can add an external hard drive and run games from it (huge plus) and it has the Halo and Gears of War franchises if you're into that (which I am). Also, it's got backwards compatibility now (limited, but focusing on titles most people probably have or would want).
PS4 however, is a smoother OS, better hardware, has the Uncharted series, and I love the newer Ps4 controllers, which are dramatically better than the old PS3 controllers. Miles of difference on the controllers (for me, anyway). That said, the X1 controllers are actually pretty decent as well.
Owning both, what I do is get the "big, serious" games I plan to invest time in on the PS4, (such as Fallout 4, Destiny and CoD:BO3) and everything else I am slightly less serious about on the Xbox 1 since it has the space for it (ironically, I got Batman: Arkham Knight, Mad Max and Star Wars: Battlfront on the X1 and have been playing them to death).
All other differences are superficial.