Both are basically the same. The only difference i have seen between the two is the shadowing/rendering on ps4 being slightly better. People still have misconceptions about both consoles such as xbox one not having 1080p which is wrong.
Ps4 has had more service issues, xbox has had compatability issues such as adobe not working for IE for months.
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They are almost identical,the PS4 just has more RAM and a somewhat better GPU. But since they are so identical you will hardly see any difference between them in multiplatform releases,although it was kind of funny that the Witcher 3 ran better on the Xbone on launch. I played the Destiny demo on the Xbone after playing it for months on the PS4 and I did not notice any difference even tho it is in a slightly lower resolution,and I have to admit that the Xbone controller is better than the PS4 one. Networking also feels like its better on Xbone,unfortunatly no Hawkmoon yet.
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It took removing the kinect to get games to play at that better quality though.