Why does my mom's iPhone seem to have better speaker quality when connected via Bluetooth than my note 4? We have a bose soundlink color, and I use Google play music on my note 4.
My recommendation is compare sound using the same media such as loading the same audio file onto both devices. Disable all equalizers and then compare. Do the same using an audio cable rather than bluetooth. At that point you should be able to tell the difference in audio performance between the to and decide for yourself if what you're hearing is due to the devices themselves or the audio source.
There's a graphic equalizer option in the "Google Play Music" settings. It lets you adjust the treble, bass and mid range frequencies and provides an assortment of 'canned' settings to match your music tastes. Have you tried making adjustments there to improve the sound quality?