Is it the player or earpiece that is more responsible for the sound quality in a smartphone?

In my experience it's always the hardware unit that seems to be problem as far as sound is concerned.

Hardware Hardware plays the important role when it comes to the audio output to the unit. So earpiece and the material used inside earpiece decides how sound renders.

The type of earpiece also plays role here. Classic earbuds are comfortable for your ears however they don't block the noise. Hence in terms of noise cancellation, in-ear earbuds offer better output even in noisy surrounding. You'll also notice that bass and treble sound different in these two types of earbuds. Another variation of headphone is over-the-ear which closes entire ear region. And those can also present a better output.

Option 1I'd suggest trying either Sony, Samsung or Nokia earbuds and test it out. You'll find the difference in audio immediately. And then buy the one that gives good audio output.

Software Controls Audio player (be it desktop or Android app) helps manage the sound variables such as bass, treble, pitch and BPM apart from volume. However that should not affect the quality of the audio output that you get. Regardless of any app, the output needs to sound good in earpiece. However software itself can't affect much of the output so it largely depends on the hardware i.e. earpiece in this context.

Options 2 You can uninstall the player and install the one that gives more control on sound variables. My suggestion is to try Poweramp or Black Player. However after playing with few apps, you'd find that issue with audio is largely hardware dependent.

Well, it depends both on the software and the hardware. By Hardware, I mean the material used in the headset and the earbuds. Opt for a good headset from the reputed manufacturer - like Sony and Nokia - that are known to ensure quality in terms audio performance. Also the type of earbuds plays an important role here.
The music player in your smartphone also needs to work hand in hand with your headset. Ensure that the original music file you have on your phone is actually in high quality. Consider installing a new music player that offers you additional controls for you to manipulate the audio quality.

Some of the aspects that affect your music experience can be

• Audio Source - The bit rate and sample rate are the two parameters that need to be high enough. Check if your audio file conforms to the requirements. Your bit rate should be at least 128 to 256 kbps.
• Your smartphone software/hardware - Your default music player has a great say on how your song will sound on your headset. Check out the alternatives you have. Choose a player that offers you the kind of controls you wish for. Poweramp and MX Player are a couple good examples.

Every mobile phone has its own music device and ear piece. The software which comes in build-in function will differ in each phone. In most cases the phone and ear piece should be well balanced in order to produce good quality songs. If you see, in some phones, other model's earpieces are not accepted. It is due to its base sound quality. For this, I can give you some tips. Try to update your music player. Not every Smartphone will provide you an earpiece with the handset. So, you need to buy an earpiece from outside. Better purchase high quality of earpiece models like Philips, Sony, JBL etc. Basically these types of models give you better background quality of music and adjustable equalizer according to our taste are also available.