The UI for those who don't want/use Apple Music or Radio is poor, not because it's new but because it compromises ease of use.
(1) Now that we can't edit the bottom "tray" (for lack of a better phrase) I have to use the pull-down to select between Artists, Albums, Songs, Genre, etc. These used to be at the bottom for easy access ... now these are in a pull-down, but what makes that worse is that I have to scroll
all the way to the top just to see the pull-down (assuming that my last selection was not at the top).
(2) The "Recently Added" feature is OK, but it takes up
way too much valuable space, and could have been a button (equivalent to "Playlists"). Again, these buttons' location/presence should be user-defined, as was available in 8.3 and earlier.
(3) Access to Now Playing is a skinny little ribbon at the bottom of the screen, not so easy to tap accurately under some circumstances.
(4) When in a playlist of mixed artists, sometimes I'll want to play the complete album of the song that's playing. I used to be able to flip Now Playing over to see the album's entire track list to choose from, and playback would stay within that album if I selected a different track within that album. There is no equivalent for this in iOS 8.4, so now I'd have to navigate to the album via the silly pull-down at the top (see #1).
(5) Lyrics appear to be gone entirely, that was a nice feature.
(6) No indication of "Track x of y" ... sometimes nice to know how far into an album or playlist you are. The new "Up Next" feature helps, but isn't really the same experience (though I do like this).
(7) Smart Playlists
still won't Live Update if you use the "Playlist Is ... " criteria. I've given up on this capability ever being restored in iOS, even though it works on an iPod Classic.
I've submitted feedback to Apple on each of these issues, but skeptical they'll be addressed.
http://www.apple.com/feedback/iphone.html