In my experience so far, the SQ of the iPhone 5S is definitely headphone dependent--and I'm not talking hard to drive headphones vs. easy to drive--even among the easy to drive phones, there is a big difference in synergy or compatibility or however you want to describe it.
With my Sennheiser HD-595's, Sony MDR-7506's, and my Etymotic ER-4S's, the treble is anything but "messy" and "splashy"! Aggressive? Maybe a bit. Forward? Yes. But not messy. I find it to be brilliantly clear and precise and defined. I absolutely love it.
But with the Sennheiser PX100's I think I would agree with "messy" and "splashy" or maybe "harsh" or "aggravating".
So, for what it's worth, in my personal opinion / experience, you need to chose your pairing with the 5S way more carefully than with the 4--with the wrong headphones, it borders on unlistenable. But with the right headphones, it's awesome--way better than the 4.
In my opinion anyway!
Point is, for those reading this, if you're considering getting a 5S then I would definitely recommend bringing your preferred headphones with you to audition it.