Not in my experience. Exiting out of games to apps and back on PS4 is sluggish as hell. And its smooth on X1.
It doesn't remember passwords on websites etc..
The only thing that Sony's OS kicks Microsoft's ass on is installs. Imo
Not from my experience. Everything seemed more sluggish on the X1.
More problems that require hard reboots while my PS4 never did.
You can't even bring one party to another on the X1. You need to exit, re invite everyone.
Installs take longer, party chat issues...