OK. So my listening fatigue with the 5S was definitely due to my alergies / inner ear fluid issues. The symptoms distinctly manifested and I took allergy medicine and the issue is waning, and so last night I was able to spend some quality time with the 5S without fatigue or discomfort (although I'm still not 100 percent, so I'm classing my findings here as preliminary).
And, I am impressed. As others have said, the 5S seems to be more "detailed" with better definition, especially in the bass, and more aggressive--i.e. more "dynamic". It's subtle, and like others have said, there aren't big difference between various generations of iphones and ipods, but they still exist and they still matter to many people, myself included.
What is a lot more objectively ascertainable, however, is that the 5S can definitely handle harder to drive (and/or go louder with them) headphones. From A/B testing, I found that my 4 was noticeably less able to drive my Grado SR-225's and my Sony MDR-7506's than my Apogee Duet. And I should note that neither of these phones is "hard" to drive! Meanwhile, I found with the 5S that it really did a very good job at driving both the 225 and 7506. The sound was better with the Duet, but not a lot better. Only just noticeably better, no more. And I have my volume limit set lower than on my 4 for the same loudness. So, in my personal, not-very-strict testing, I have found that the 5S can go loud and drive harder to drive headphones than my 4. On the flip side, I'm not that thrilled with the sound of the PX-100's out of the 5S. I think it was also flawed out of my 4, but the flaws out of the 4 didn't bother me much--bass was a bit soft and undefined, loss of details in the treble, not as good with dynamics.
Meanwhile, I'm thrilled with the sound of the 7506's straight out of the 5S. Really dynamic stuff like well mic'd and recorded drums, acoustic guitars, fast synth, etc., is wonderful to listen to straight out of the 5S.
I'm very much looking forward to hearing what the ER-4S sound like out of the 5S, and I think the higher impedance (100 ohms) will only help matters given that the 5S can and will drive the ER-4S's loud enough.