Essentially, the real advantage here is paying for the premium version and getting YouTube Red -- which then opens the door to ad-free streaming (videos and music), offline viewing, and (confusingly) full access to GooglePlay, which is a streaming music service itself. From there, you can take advantage of YouTube's distinct position as a sharing platform: the remixes, the covers, the live versions, and songs that might be barred from other streaming services will all show up here on YouTube Music -- which is a major plus that other apps like Spotify and Apple music just can't compete with.
What YouTube is doing here, is playing to its strengths, and translating that into a streaming experience. Is it enough to persuade loyal Spotifyers to make the jump -- just for some video access, and maybe access to a slightly larger catalogue of music? That remains to be seen. But given YouTube's track record of unparalleled success, I have confidence they will at least put up a worthy fight.