For a start: the UI.
I know Apple Music gets hate for it's UI but it's nirvana compared to the horrible, grating, death by 1000 papercuts UI that Spotify has.
So that contributes a LOT to my impression of Spotify.
I find their radio offerings better than Spotify, and the curated playlists to be of higher quality and better variation. The For You tab alone is better than a lot of what I found on Spotify.
The importing of my existing library and linking of it into the service with all sorts of metadata made for a seamless experience that I haven't found from any other service either.
Basically... it's just a little bit better (for me) in every possible way, while being nicer to use.