It's more about dynamic range. If you don't provide the headphone with enough clean power, bass and other parts of the audio can suffer, regardless of how loud it can seemingly get. My work iphone provides plenty of power, but my Nexus 7 and Nexus 4 headphone jacks do not, especially when I have Viper4Android audio software running. Running through a decent DAC, and a small amp gives the best results for me on those.
Been A/B ing the EFI82-MT and 489, and I like them both. The EFI is the better value right now though, as it can be found for ~$35.