In my opinion the XBONE wins the war in terms of interface with the PS4. Vocal commands are also really cool, so that's a nice addition as well.
I'm not to familiar with the Ps4, but the new xbox one dashboard I don't like. I've had the newest dashboard probably 4 or 5 months before it was released to everyone and had to deal with the glitches and bugs it had. It was fixed perfect the few weeks before launch then all hell broke lose. I still find lots of party chat glitches happen when trying to do commands to fast also.