I've been battling with this too ... after years on Android I've used GPM and I have several family members associated with my account so when I switched to iPhone I stuck with it. Wanted to try AM so I'm running with (and paying for) both ATM. Love built in lyrics with AM, customizable EQ and the randomized "for you" seems to offer a wider variety of music then GPM's "feeling lucky" does. Obviously the integration with AM is far superior too ... but I think I still prefer GPM. Likely due to the fact I'm so used to it, but AM feels clunky to me.
For instance, if I want to know more about an artist or an album with GPM it's right there when hitting the menu (three dots) button. With AM you have to touch the highlighted artist name, which takes you to the album then touch the artist name again to get to their page and then scroll all the way down to the bottom to read about them. Seems like a lot of steps ... maybe I am missing something that'll get me there faster.
There's other little things too ... like if I'm listening to an album on AM and like (or dislike) a song in order to register it I have to open the app, hit menu then hit love or dislike whereas with GPM as soon as you open the app the thumbs up or down is right there.
GPM just seems more comfortable to me ... likely due to years of using it. YouTube Red is a nice bonus too. In the end I'll likely end up keeping GPM because of all the family members that are associated with my account. But will likely try AM again once iOS 11 drops ...