Apple Music does not work properly eb´even in Safari (in Chrome it does)
I've found this as well. The last version of Safari that runs under El Capitan on Mac Pros won't really run Apple Music's own website, which I agree is ridiculous -- I use it with Chrome as you do.
I don't know about you, but Apple Music isn't the only thing that doesn't function very well (or at all) in El Capitan for me anymore -- I've had lots of issues with Safari, Mail, and syncing with iCloud.
I have only a little experience with other services (and I miss Beats dearly), but Spotify has by far the largest collection outside of Apple Music. Tidal is higher quality but a more focused library. I think for any sort of Apple-style syncing features on Spotify you need their Premium service.