It's fugly, for starters. (iTunes desktop) Things are very hard to find most of the time. Sometimes when you do find stuff, you still can't play it, even though it appears to be in their library. (Do a search in AM for "Joe Jackson Heaven And Hell". Then try to click on the result offered.) Then there's the tiny text, columns you can't resize and loads of whitespace you can't do anything about.
I am surprised there seems to be no decent alternative to Mac iTunes. I looked around and the only that wasn't gross was Tomahawk, but Tomahawk is even stupider than the iCloud sync – it takes an album title and tries to guess what is on it, instead of displaying what ACTUALLY is on it. 1-track singles turn into 18-track albums without the actual song present. At least it doesn't butcher my library, but that's hardly a reason for me to use it.
As for decent alternatives to Apple Music itself, I am very happy I haven't cancelled my €4.99 subscription to Spotify because they removed the option and now you have to pay €9.99. But existing users continue paying €4.99 (at least until Spotify removes the option from us as well). In any case, Spotify beats AM in every aspect except for the fact I can't set up Spotify on my phone to play both streamed and local tracks, and having two separate players is a bit silly. AM would win here if not for the fact it destroys libraries and refuses to sync tracks for many, many people. (And that the Android app never materialised.)