Maybe the coolest feature Spotify has that Apple Music apparently doesn’t have (yet) is the social aspect: You can see what all your friends are listening to, and get suggestions based upon the friends you really trust.
Also, Spotify recently added a cool running feature and a new video content initiative. Which is cool, I guess.
Spotify has player, which, duh, come on Apple.
Apple Music extras
Apple Music’s big differentiator is Connect: A section of the app that lets you keep up with your favorite artists. It’s a little bit like a Facebook page that you can follow. The artist posts something, and you can respond to it. The artist can also use Connect to share exlcusive content.
Apple plays nice with all of the content you already own. I have probably 100 GB of music uploaded to iTunes Match and I can grab it from any of my Apple devices on the fly. I like the looks of how Apple Music plans to deal with integrating your personal collection with everything else. (Google Music also works well with your personal music collection.)
You shouldn’t underestimate how lazy people are. Apple already has hundreds of millions of credit cards on file. Many of these people will probably end up subscribing to Apple Music like the good Sheeple they are.