Both systems record your gameplay and allow you to share it online and show off your skills, however PlayStation 4 users will have to rely on the automatic 15 minute recording which, while it works, has the problem of you having to stop playing to save the footage.
Something which could be deadly in an online game.
However on the Xbox One the game will automatically save all your good moments such as goals, saves and hopefully classic moves. Then after the game you can decide to keep whichever ones you want and share them as you see fit.
That’s some proper next-gen technology right there