My main issue is that Apple doesn't have anything remotely comparable to the Discover Weekly list. Apple's "New Music Mix" just contains recent releases that Apple thinks I might like. Spotify's "Discovery Weekly" OTOH also finds many older songs that I have never heard before, and usually 80% of the songs are spot on for my taste. I don't know how they do it, but it just works fabulously well for me. Apple's other mixes ("Favorites", "Chill") are nice, but useless for discovery, since they mostly (or exclusively?) contain songs I already know.I'm not saying you'll experience the same thing as I have, but the longer you stick with the service, the more the service will cater to your musical tastes.
Besides that, if I want to explore, say, a new genre or artist, I love browsing all the user-curated playlists. Beats every algorithm I have seen so far. Again, Apple has nothing comparable.