The most
important feature (IMO):
Settings > Music > Show Apple Music
I applaud Apple for putting that in.
The new music app is very overwhelming. Lots and lots of little things here and there are gone, and even if you've turned off the Apple Music stuff and are not signed in, it still presents your stuff as if you are and shows you icons that are unnecessary.
The new audiobook integration in iBooks is interesting though. It broke my playlist organization and you can't take advantage of the new "loved" button, but then now I actually have a reason to use the "Genre" field and can make the Categories tab work to my liking.
The controls are much nicer than those in the music app too.

You can customize both forward/back skips separately, and by 10, 15, 30, 45, and 60 second intervals.