Thanks for the info on the ety ER-4S everyone! Much appreciated. As for "burn-in" on the iPhone, yeah, I didn' think so, and I haven't noticed any change. Just thought I'd ask to make sure.
I think--I'm hoping--that all of my issues with the 5S are due to alergies. I've been freaking out since I have only a limited time frame within which I can return the 5S, but ultimately, I just can't believe that the differences between the 5S and the 4 could be that great. Plus, we have various reports of improved sound quality of the 5S. SO . . . I think this listening fatigue is all in my head--or my inner ears. LOL! And even if it's not I'll just find a workaround--maybe an amp, maybe new headphones, or maybe both. Or maybe even a separate DAP. At this point I really don't want to go back to my 4 (which is on its way to a friend overseas), as iOS 7 takes a lot more resources and is (arguably) really only well suited for a 5 or 5S at this point. YMMV.
Back to more objective aspects of the 5S:
What I can report is that iOS 7 has a reworked music player app, and there are, at present (7.0.2) three significant losses of functionality:
1. When viewing your collection by artist, there is only ONE sub-view: ALL SONGS grouped by album. Previously, when selecting an artist, you would then see a list of albums. Then if you selected an album, you would see the songs on that album. Start with the first song on an album and it would play just the album, ending playback on the last song. Now, if you select an artist, you see all songs grouped by album. If you select the first song of any album playback will continue on through the last song of that album and into the first song of the next album (assuming it's not the last album in the list). I find this to be inconvenient. For some artists I have DOZENS of albums, and scrolling through all the songs is tedius and inconvenient and time consuming. Album view is ALPHABETICAL, so that's no help either.
2. Furthermore, cover-flow is GONE. Now, in land-scape orientation, you get a 3x5 (on a single screen--it scrolls left-right) matrix of album covers, each one about a thumb-width to a side. I am finding this to be much less convenient and a lot less aesthetically pleasing than cover flow, although to be fair, I never used cover flow very much.
3. The video player only lists music videos ALPHABETICALLY. That's it. I have 100 music videos. It's a lot less convenient to have to scroll up and down this big long list. In iOS 6, any artist in your collection with 3 or more videos would appear as a single entry in the main list. Clicking on the artist would bring up a sub-list of all their videos. But, no longer. And if you give your videos their own album title and a track number so that they appear in the music app, they can now only be played in portrait orientation. Rotating to landscape brings up the matrix album view. So that's not a workaround.
None of these is the end of the world or a deal breaker for me, but I do really hope that Apple brings back the functionality that was lost with future iOS 7 updates. But I'm not holding my breath.
OK. Thanks everyone for putting up with me! I'll report back on my assessment of the iPhone 5S audio out sound quality once my hearing returns to normal.