The main reason I updated the phone was to be able to take a look at Apple Music. I still have an iPad that is running the old version, so if the wheels came off, I could still listen to music.
Below is a quick video showing the new Apple Music app:
A New Look
I never felt that it was much of a hardship to figure stuff out on my own, but if Apple wants to continue adding subscribers that have never used a music app in the past, they needed to dumb it down a bit and make things more simplistic. They have done that with titles in your own Library section that tell you exactly what is behind each link. You can even edit the page so that it contains even more or scale it down to just what you want to see (they require you to keep at least one item in the editable list).
Their "For You" section once had playlists and albums blended together into one mishmash (that I actually liked), but now the page has defined sections for suggested playlists, stuff you listened to recently, and much more.
The "For You" page is still there, but it is no longer the landing page.
The "New" page is replaced by "Browse" which is probably a better description since it contains more than just new music.
The Radio page is still around, but they no longer have a tab for Connect. Instead, Connect can be found at the bottom of the "For You" page. They also added a tab in the bottom row for Search rather than having it at the top right corner of the app.
They also added lyrics for some songs. Right now, we are in beta, so there are still a lot of missing lyrics (it took me a while to find the example in the video), but I expect that will get better as time goes by.
The also added an "up next" area below the album art for the music that is playing. You can also move songs up and down the "up next" section. I had a playlist with hundreds of songs and it loaded at least 150 (if not more) of them.
The "Search" section now keeps your last three searches. This is very nice since I often want to revisit a search I did at home when I get to work. They also have trending searches that give you some idea what others are listening to.
The Genre section on the "Browse" page now has "Genres You Follow" at the top.