IPod shuffle vs iPod touch sound
Well both use a different audio chip, the iPod touch (4th & 5th gen) outputs audio in digital signal vs analog on the iPod shuffle, plus if I remember correctly the headphone jack on the iPod touch 5th gen has a lower power output vs the iPod shuffle. I've also noticed a loudness difference on my 5th gen iPod touch between iOS 7.0.X and 7.1.X so that might be a contributing factor why it's not as loud. As for the lumia 820 I'm not sure.
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