Do exclusives matter to you? If you are playing multi-plats, I would go with the PS4 because it has a larger install base. 2016 should be the first solid year of steady exclusives to release for PS4 as well.
If you play only shooters, Xbox One is better. Xbox Live is a bit better reliable than PSN, but not as much as 360 versus PS3 was.
They both do the same thing. PS4 is a bit more powerful hardware wise, so a lot of multi-plats have higher resolution and more stable frames, but developers are still figuring out how to optimize on both systems. Xbox One multi-plats will probably catch up eventually, like PS3 caught up with 360.
Some people take the controller into consideration for genre specific games. For example, a lot of people prefer fighting games on the Playstation pad because the D-Pad is larger and considered more reliable for inputs. Conversely, many preferred the 360 controller for shooters because the trigger buttons are better than the PS3.
At the end of the day, it just comes down to what games you want to play. I picked a PS4 first because I know I want to play Uncharted, Gran Turismo, God of War, Ratchet and Clank, etc,. Xbox One has Halo, but I won't pick up the console until more games come out that I want.