The issue is the Digital-to-Analog Converter (DAC). Older classics, though the 5.5, used DACs from a company named Wolfson. These are considered to produce a "warm" sound and, generally, these models are considered to have the best sound. The 6th and 7th gen Classic as well as most of the iPhone and iPod Touch families use DACs from Cirrus Logic which many feel produce a more "analytical" sound.
This is a situation, though, where YMMV depending on headphones/earbuds, your own hearing, etc.
Thanks for that information! This is what I wanted to hear, discussion of the manufacture and technical specs of the DACs that produce the sound on the iPods/iPhones!