Spotify also has a native(-ish) OSX client (can you use Google Music outside the browser?) and excellent playlist drag/drop and sharing support. Plus, I love their iOS user interface. No other service has come close in either area.
A couple of years ago Spotify rewrote their clients to use CEF (Chromium Embedded Framework), so since then their clients are in some sense native and in some sense not, and much more consistent across platforms.
Anyway, I agree with you that they have been pushing the envelope in terms of mobile functionality, especially iOS. Lately I'm not happy with how Android has crippled their lock screen experience by screwing up the lock screen widget API - but that's not Spotify's fault.
To any Spotify skeptics, I highly recommend trying the premium service. The social feed, cross-device sync, BPM matching for runners, collaborative playlists, Spotify Connect (ability to switch and control music playing on another device), Algoriddm Djay integration, all changed the way I experience music. Their radio/suggestions engine is not as good as Pandora's, but is slowly improving. The only thing that is sort of a letdown is the visualizations API, but I can see why it's not a priority.
> A couple of years ago Spotify rewrote their clients to use CEF
Eh. And not to sound like a cranky old man, but that shit sucks.
It's ridiculous that their "app" needs 20-30 seconds to boot on a modern computer. It's a damned music player. Plus, when the machine is under load, it skips like a 1993 disc player. And the damned thing crashes routinely.
Pre-CEF I was terribly impressed by their mac client. It's been a pretty ugly cliff they've fallen off though. They did a developer blog post some time ago detailing how teams are all using separate JS routines and libs... and I have to say, I wasn't surprised. It's rare that a popular app regresses in performance and usability quite as much as they have.
You have to use 3rd party apps to get Google Music outside the browser, but it's still essentially just using the regular web page with the addition of being able to use the media keys.
It requires a bundled by default, Google Music app. If you disable or delete it, the media keys will stop working. Here is the download link for the app :
I just wish they had better local file support.