To give myself a fair comparison on Apple Music and Spotify and also to see if perhaps Spotify might be the better music streaming service for me. I decided to spend a day with Spotify, I got a 7 day free Premium trial on Spotify (which I thought was a bit on the greedy side).
Yeah, I managed to find an album on Spotify that wasn't on Apple Music (and vice versa too I found when looking for another album, but to be fair, Spotify has been on the go a lot longer). But that aside, my first impressions were not good at all with Spotify, I really didn't like the UI on Spotify. I found it not at all intuitive and I'm usually pretty quick at figuring UI's out and finding my way around an app, but after spending the day with Spotify, I was still struggling with it. In comparison, I managed to find my way around the new Music app (on iOS) pretty quickly and only looked around online at some of the guides to see if there was something I'd missed.
Another thing I missed was how you tell Apple Music what you like, artists, genres, and I couldn't for the life of me find a similar feature on Spotify. Yeah, I'm lazy and I like the way Apple Music presents me with stuff without the need to think what should I search for (which I'm guessing is how Spotify suggests stuff for you).
Also with regards to sound quality. When I was using Spotify, I chose the extreme setting for sound quality (which gives you the highest quality). I chose the exact same album on Spotify and also on Apple Music. I found on Spotify, the volume level was a tad lower (despite having the volume set on the same level) and good as the sound quality was on Spotify, to me, it lacked a bit of detail/clarity when compared to the sound quality when I listened to the same album on Apple Music. Apple Music uses a slightly lower bit rate than Spotify from what I've read, but I think Apple Music uses AAC file format. Definitely for my ears the sound quality from Apple Music was noticeable better.
Apple Music won't be for everyone that's for sure, and the same for Spotify, but I cannot see myself considering Spotify for my music streaming service after what I have experienced.