I have both.
The PS4 is overall the better console. Here is my little breakdown.
If you like to stream games. PS4 does Twitch + UStream, XB1 does Twitch.
Like to record video clips and share?
PS4 can share direct to Facebook, Youtube, USB drive.
XB1 you have to upload them to OneDrive and then manage them seperately.
Clip length? PS4 persistently records 15 mins. XB1 limited to 5.
The PS4 interface is a lot snappier most of the time. It bounces between dash and games instantly, between menus etc
XB1 is faster for messaging and the accompanying Smartglass app is better but feels a bit disjointed. Every element of the system i.e Friends, Messages etc runs from a seperate app. It isn't as slick as the PS4.
Both handle party chat well. The XB1s is a tad buggy at times.
As for the meat and potatoes..... games.... the PS4 in every instance so far (from what ive seen) serves up a higher frame rate and usually a higher resolution.
The PS4 controller is very good, love the touchpad function for typing messages but suffers from a poorer battery life. The saving grace is the built in battery.
The XB1 controller...well. The thumbsticks feel a step back compared to the 360 imo but it does feel good in the hand. With the play and charge kit \ clip in battery, it offers pretty insane battery life. 10+ hours.
Overall.... the PS4 is the winner for me. I will be picking up exclusives on the XB1, but most of my multiplatform love will go to the PS4.