The HTC player sees the music on your device, but not in the cloud. The Google player sees the music on your device and in the cloud, but with one caveat: only if it's Google! If you have the Amazon MP3 store and have music in that cloud, Google won't see it. If you have Google save the music to your device, from their cloud, it will see that but not music you've saved to the device on your own, or through Amazon. The great thing is that you can upload roughly a bazillion songs to Google for free in their cloud player so your entire library is pretty much there. Then use the cloud player to download any of them to your device. Not just ones you purchase from Google, but any song you upload to them. This would include that stuff you felonious-ly got from Napster and Limewire back in the day. But Amazon is great to have as well, because they have some ridiculous sales.
If you want one solution, go with Google. Upload everything to their cloud. Buy it from them, Amazon, whoever. Save it to your PC (which I assume you do anyway so you have a full hard copy of your library) and then upload it all. Listen to everything through Play Music and download to your phone, through Google, any songs you want access to when you don't want to, or can't, stream.