I got to this thread searching for iPod 6G sound quality issues (as I've heard about them off forum). I'll try to address a few things speaking as an EE.
The transfer function of a system (amplifier, filter, etc. - not necessarily electrical) is described by the amplitude response and phase response. You need both to fully describe the system - neither gives you the full picture. Actually, even both together still don't describe everything - they are a mathematic construct and it is often forgotten that in real world there are issues that will affect the output signal yet won't show up in the transfer function - e.g. jitter. Group delay, as mentioned, is a derivative of the phase by the frequency. Therefore if the phase is linear by frequency, the group delay will be constant.
An ideal amplifier would be the one where its amplitude response is constant (flat) - equal to the amplification factor, while the phase response is linear. Such a system will not introduce any distortion (if you give it 1kHz, you won't get any harmonics at 2, 3, 4 and so on).
A lot of attention has been placed on the frequency response for many decades. Ironically, solutions employed to keep frequency response flat usually do so by sacrificing phase linearity - especially when talking about filters.
Some people - including ones I trust - say that nonlinear phase response leads to audible artifacts. This is one of the reasons some audiophiles shunned digital - and still do to this day. They typically talk about harsh, unnatural digital sound. The situation has improved with years with better DACs and better designed filters but started reverting back to "bad" with the proliferation of portable devices and "price is king" attitude prevalent with consumers today.
Now, when you design say the DAC output filter - the one coming after DAC chip and before the headphone or line amplifier - you are trying to create a filter with amplitude response that ideally drop to 0 past 20kHz but stay flat until then. For practical reasons you need the filter to be of low order if it's implemented as analog. You can get very nice amplitude responses from some filters - but most filters that do justice to amplitude response have bad phase responses (e.g. Chebyshev filter). When I designed DACs, I opted for gentler filters that keep linear phase (Butterworth? I think) - which could have as much as few dB drop at 20kHz (I usually aim for 0.5dB) rather than using steep and deep filters. Attenuation of D to A process artifacts in the 100+kHz range is still sufficient, but you get the gentle rolloff in the audible range (<20kHz). Most companies want the response as flat as possible because that's one of the most often quoted and measured parameters, so they would opt to keep amplitude flat at the cost of non-linear phase.
What I don't know is how audible is this. I do believe in it, but I'd say you would need to listen critically, with good equipment. Using lossy compression, subpar headphones and no headphone amplifier - not to mention noisy environment - I wouldn't expect this to jump out at anyone.
On the plus side for new 6G, from the graphs in this thread it looks like the amplitude response stays fairly flat when loaded with 32Ohm headphones, unlike the old one. That implies a good headphone amplifier that is able to keep up. I would imagine this would definitely be audible as tighter bass in 6G.
For the record I've been listening to iPod classic 6G since I got it in Japan on vacation (here in Canada they are still not in stores!!), and with only nero-encoded ~172kbit/s AAC on my (also bought during this Japan trip) Audio Technica ATH-A900 and I haven't had complaints. Perhaps I'll plug these headphones into my Flute 2 DAC/amp and compare with 6G using lossless.
Also, Cirrus makes some nice DAC chips such as CS4398 or CS43122 I used. These are high end audiophile chips. They also make some very crappy chips from what I understand. Just like Sennheiser makes some really crappy headphones.
