Great question.
I'll be going from a 5 to a 5S. My 5S should be here in the next few days.
I'm guessing the main thing people will notice is speed and camera quality.
I'll doubt you'll notice speed of general use. When it comes to iphone 5and 5S, I imagine the limiting factor is more the UI itself, in that it's programmed to animate in a particular way.
I don't think the iPhone 5 is operating at the limits of its capabilities in most cases to make the next gen processor do it faster.