Man, these consoles have been out for 18 months or so, and we've never had a thread on this come up? No, wait, we've had probably two dozen.
I picked the Xbox One, and for several reasons (I'll just start listing them until I get bored):
1. I trust Microsoft's online security more than Sony's, and having not suffered any issues during 11 years (at the time, now 12+) of having LIVE, I just prefer that online system.
2. Nothing Sony offers as an exclusive touches Halo, for me. Killzone is sub-par, and after nearly 14 years since I first played Halo (man, it's really been that long?), I'm in until the end...I think.
3. Gran Turismo 4 was the last time I touched that franchise, and I didn't like the game AT ALL. Forza 5's content issues aside (which are being remedied this year), it's still a fantastic racing franchise I have no reason to give up on (again, now that the full-game content is back).
4. I've long preferred the Xbox controllers to PlayStation ones. I didn't like the PS4's triggers, and I prefer the larger Xbox controllers and their offset sticks.
5. Sony's bread and butter has been the third person action/RPG stuff, and it's not my gaming wheelhouse. The shooters and racers where Microsoft prevails suit me better, and there are plenty of really good third-party, open-world action/RPG titles to enjoy (where as the third-party FPS options have gotten worse of late, as CoD turns into an ADHD nightmare and Battlefield ignores stability).
6. Windows 10 is going to allow for some cross-platform gaming with PC and Xbox users (Killer Instinct and Fable Legends are the only games thus far). It also involves a somewhat consistent ecosystem across PC and Xbox (and mobile, hopefully), and that's generally nice.
7. Everyone I game with is on the Microsoft platform.
There are more things, I could sit all day and compare things, but it's personal preference. Microsoft's the go-to console if you like shooters and racing games. Its online service is older and more stable. Though the Xbox One's UI is far from good, it's at least controlled by a company with several decades in the OS market, so I expect a better OS and user experience with the Xbox One's software, especially with Windows 10.