The iPhone 5S looks identical to the iPhone 5. It only has a beefier 64bit processor and M7 co-processor, Touch ID and an improved camera to start off with. But it also has something else that wipes the floor with the 5 and older 4S/4 iPhones.
The iPhone 5S has a new audio codec and class D amplifier by Cirrus Logic. This incorporates the digital to audio conversion of the MP3 tracks and then powering your headphones or the inbuilt speaker.
The difference in sound quality is night and day with superb range, dynamics, punch, separation and clarify.