I haven't used Pandora in a long time, but I have to say that everything you mention can be applied to my experience of Spotify's discovery/radio features as well. Plus it handles playing songs on-demand.
I can't seem to get spotify to recommend me anything besides rap music. I use the checkboxes to indicate I like classical, the Dead, Phish, Dylan, Cash, and more but I have never once had anything besides rap music show up on my discover weekly. It's a bit frustrating.
There's recommendations at the bottom of individual playlists now so I can look there but still a pain that I can't get a nice mix in my discover weekly.
The most important thing for Google Play Music after the "upload your own stuff":
It does a great job caching songs ahead while you're on Wifi, so you can minimize data usage while out and about. Plus, with the caching it also works offline perfectly well.
I feel a bit sorry for all the other services, but on a technical level Google Play Music has outplayed them all entirely.
Oddly enough I love GP's recommendation set so much more than Pandora's. It's so much better attuned to what I like and don't and what I like to explore. It's very good at distinguishing what I like and what I don't, and I'm pretty picky about what I listen to.