I'm sorry, but did I mention buying a new phone? The fact that you think buying a different Android phone can increase sound quality means you have no idea what you are talking about.
Except it already is "right" when it's mastered. At least, that's the ideal for producing music. If something is loudness mastered to begin with (compressed and made loud as because people are idiots) then you can't use a DSP to fix that. You also can't add bass to ty headphones. Think of a car rattling when someone installs a sub and how terrible that sounds. The same concept applies here.
This doesn't boost the sound. It gives you a bass heavy unbalanced sound that will sound terrible on anything that doesn't have nice bass properties to begin with. If you want to boost how something sounds then you need an amp of some sort. This is a basic one:
Amazon.com: FiiO E5 Headphone Amplifier: Electronics
Placebo effect and people not knowing any better because they've never heard better sound quality to begin with. Example: Anyone who thinks ipod earbuds sound good, buys Beats products, Bose products, or Skull Candy products.