Got my hands on iOS 8.4 - the update notable for its music improvements.
First of all, the music app updates are fantastic so far. It looks better and it's way more functional. As a full-album listener, I appreciate the changes in how my collection is structured. It's much easier now to find an album and play it on repeat without having to go through too many screens. That was something they broke with the introduction of iOS 7, and now things are better. I like that recently added music is brought to the forefront.
I tried out Beats1 for about 20 minutes. The music is mostly garbage, but I get what they're trying to do. It's like having a truly global terrestrial radio station available over the web. I still have a soft spot for radio with actual DJs and live broadcasts, where the songs are chosen by people instead of computers. I hope this catches on and they expand it to more genres/formats. I would love to have a station like Beats1 that plays music I like.
The streaming radio stations that were already around are still there - but I read there have been some tweaks so I'm trying them out again. I listen to more indie than anything, and one of the biggest gripes I had with their indie stations from before was that they divided everything across three stations and there was no way to blend it - so I had to decide to listen to Indie Rock, Indie Pop or Indie Electronic. I had no way to get a good mix and hear new music. Now it seems that there is a station that is just "Indie". It seems OK so far, and perhaps a bit closer to what I'm looking for, but the jury is still out.
I'm eager to dive into the part of the service that's supposed to compete directly with Spotify and Rdio. I'm a Spotify Premium subscriber, and I use it chiefly to test drive albums before I commit to buying a physical copy and adding it to my collection. To me, a tangible product and the ability to actually own the music in my collection rather than just licensing it is important to me. I'm intrigued by having everything in one app instead of two. I need to see if Apple Music has everything I'd want to play - I imagine they do, but you never know. I could see myself making the switch.