So I've been using Apple Music all day and I think I've got a good handle on what sets it apart from other streaming music services for me. The thing is, that it doesn't quite behave like a streaming service if you're already an iTunes user.
You can listen to the new internet radio station Beats 1. You can listen to any number of algorythmic 'radio' stations which are generated from a genre based on feedback you provide when you like or dislike tracks. These are both kinda neat but I wouldn't pay to have them. You can also listen to curated playlists which was one of Beats Music's original selling points. For me though the really great feature is being able to simply add albums to my existing itunes library, either downloading them or adding them for streaming (just as you can with an existing iTunes Match account). They work just like any other album in your library and you can use them to build playlists just as you could an iTunes purchase or ripped CD. It's the integration that sets it apart.
I tend to want to listen to albums, a single artist from a single genre at a time and this feature allows me to expand my listening massively, effectively completing discographies and 'collecting' albums I might not have had quite enough interest in to acquire otherwise. This will justify a subscription for me, it's really great.
As soon as there's an Apple TV update with Apple Music support then Apple Music will be absolutely functionally ideal for my needs. I couldn't be more pleased right now.