The one area where I think Google Music has Apple Music beat is that you can use Google's services with a standard web browser, you don't have to go through iTunes or an iOS device. iTunes, through Windows, is still a resource hog. It consumes even more resources than Chrome accessing Google Music and that's saying a lot (it is using 1GB of RAM on my system right now and I'm not even accessing the store, Apple Music, or playing anything back).
Having said that, I find iTunes easier to use than Google's online interface. The integration with iOS is what sold me on Apple Music. You can use both and I think they will be about equal in terms of what you're getting. Both allow for the manual online backup of songs that aren't in their services, both will offer the same audio quality, and both are solid services. But, the main thing I noticed with Google Music is that it can't download songs in the background. I have a "thumbs up" playlist that houses every song I give a thumbs up rating. I can rate a song on my system and my Note Edge will automatically download it when I am connected to wi-fi. An iPhone won't do that though, you have to open the Google Music app and leave it open for any downloads to starts.
Apple Music, on the other hand, can automatically download new songs and, if you're downloading a bunch of them, it can do so in the background without needing to be open. That was a main point for me mainly because I discover new music weekly and rate at least 30-40 tracks with a thumb up (or now, a "loved" rating).
Like I said, I don't think you can really go wrong with either but I prefer Apple Music mainly because it's integrated with iOS. Plus the family sharing is nice. My fiance and I will be paying $15 a month total for two music subscriptions instead of paying $10 each to Google. We can even add her parents to our family plan and not have our libraries cross (or her Mom accidentally delete stuff in my library).