When I open Spotify I am presented with its Overview view. The music presented there is utterly useless, after using Spotify for two years I have never clicked anything there. Apple Music starts in the For You tab, which incluses playlists, artists, albums, and songs I might like. In comparison Spotifys Overview is generic, it's something you would show a user that starts the app for the first time, but after hundred or even thousands of hours of listening to music on Spotify it still tries to shove Top Dance Tunes up my ass. After listening with Apple Music for a view days, after adding some of my favourite albums to my library, liking songs the recommendations are pretty good. It is a mixture of songs I know (but have not added to Apple Music) and like and songs I do not know and also like. That's the one thing about Apple Music, human curation wins. Playlists on Spotify often contain hundred of songs and run for hours, the longest playlist I found on Apple Music runs for two hours. They are better.
The other thing about Apple Music is the software. iTunes is a mess, but I argue that it's a better mess than Spotify on OS X. Spotify doesn't have a lot of keyboard shortcuts, you can't configure additional shortcuts and it doesn't support Apple Script. That might be ok for most users, but for power users iTunes is better. The Music app on iOS is a lot better than iTunes, because it is less cluttered. Spotifys iOS app is also better than their OS X app, but is also has plenty of weird UX. In 2015 I kinda expect that the mobile app is better than desktop version.
When it comes to music, the main advantage of Apple Music is that it combines local and cloud music into one library. I can create playlists, even smart playlists, that can contain songs from both. Spotify has support for local files, but it is primitive and I never used it. However, one thing that Apple has to work on is discovery in My Music. Currently you can only view either Recently Added or All. You can sort that view, but the current options are useless for streaming-size libraries. I am not going to rate hundreds of albums. I don't know what Most Played means in Spotify (because the list definitly does not contain my most played stuff), but Apple Music needs something like this. Not an all time most played/best rated, but more like most played/best rated in the last couple of weeks.
Sometimes I like a song from an album that has not yet been released yet and Apple Music let me add unreleased albums to my library. They become playable once released, until then I can play the single. That is a pretty great feature. (Update: However, currently this feature is buggy. For me, it worked for two albums, but for most albums it does not and I have to remove and readd the album to get all tracks into my library.)
I like Beats 1 more than expected. Based on the Beats brand I figured that it will be heavy on rap and beat-based music, but I already found one or two artists that I enjoy. It will not become my primary method of music listening, but I will tune in from time to time.
I have updated the article to reflect that automatically adding music once it is released does currently not work as I described it.