In the Options there is a choice and you can select between ''Stereo'' and ''Mono''. They look like the same, but there are two options, so what are the differences between them?
Stereo (or Stereophonic sound) is the reproduction of sound using two or more independent audio channels in a way that creates the impression of sound heard from various directions, as in natural hearing. Mono (Monaural or monophonic sound reproduction) has audio in a single channel, often centered in the “sound field”. i.e. and stereo (Stereophonic) are classification of sound. Source.
That's the difference!
Stereo has 2 sounds channels so that you can get different sound out of each of the 3DS' speakers or each side of your headphones. Mono mixes everything together and it's the same sound out of either speaker/headphone side. I don't know the specific differences for the Pokemon games, but chances are you don't need to use Mono unless one of your 3DS speakers is broken or you use some really funky old mono headphones.