I recently switched from Spotify to Google Play Music and here are my thoughts after a few months of usage. Google Play Music is Google's music service very similar to Spotify and Rdio. The All Access subscription, $9.99/month, gives you access to millions of songs just as Spotify does.
In Google Play You can upload your own songs. Basically they offer a cloud storage for your music. You can play them in any device without having to download them locally. The limit is 20,000 songs which equals around 40gb, enough for me. Hopefully they add more space later.
Can't find a song in Google Play? You can buy it directly from Google, or as stated above, buy it somewhere else and upload to Google. In Spotify if you can't find a song you're screwed.
The "I'm Feeling Lucky" station. Google Play has this 'radio station' that plays music from your listening history, your library and songs that it thinks you might like. It's awesome for those times you have no idea what to listen to.
Yes, Google Play has a music library where you can add any song from All Access. No need to create unnecessary playlists.
Their Mobile app is much better designed. To be fair I haven't used Spotify's mobile app in a long time so maybe they have updated it. Google Play Music app is easy to navigate and looks beautiful at least in the Android version.
Google Play Music is a web app. This could be a bad thing as well but I personally prefer it this way. It also means you could use any computer and log in to your account and play music without having to download a software, like Spotify.
Since it's a web app not a desktop app the control buttons in your keyboard won't work.
Sharing on social media sites is limited to just Google+. This is not a deal breaker to me since I never used the shared button when I had Spotify.
In summary, Google Play Music and Spotify are very similar and costs the same, so it's just a matter of personal preference. If you're happy with Spotify and love to share your songs on Facebook and Twitter then stick with it. But if you're not happy, especially with their Mobile app, try Google Play Music. It's free for the first 30 days. I'm a big Google user so using their Music app just makes sense for me.