Hi. I have the new iPhone 5s and have compared it's audio quality side by side with the 4s using some technical measurement procedures and of course my ears, a few different pairs of headphones and my favorite music.
I have noted below the output voltage of both iPhones at their highest volume setting while playing a several different 0dB tones.
1.14V (line level load both w/ channels driven) (no clipping)
.87V (16ohm headphone load w/ both channels driven) (clipping occurred)
1.02v (line level load w/ both channels driven) (no clipping)
.92 (16ohm headphone load w/ both channels driven) (no clipping)
As you can see, technically the 4s is louder but only with a line level load (connected to external amplifier). When the headphone load was connected, the device introduced distortion and the output voltage dropped.
With the 5s, the voltage dropped during connection of the headphone load as expected, but much less than the 4s, additionally there was no audible distortion.
The 5s does not quite go as "loud" but can drive a low impedance load with less enough voltage drop than the 4s to actually go louder with headphones attached. This also indicates better dynamic range.
Also worth noting the headphone channel separation on the 5s was a little bit better as well.
As per my listening tests, I found both phones to have fantastic sound but the 5s sounded a tad cleaner, with better imaging, timing and overall accuracy - especially at higher volume levels with more difficult headphones loads.
Edited by mdelaney1986 - 7/7/14 at 8:55pm