It has a significantly improved camera, slightly better battery life, a faster processor, and a fingerprint sensor allowing you to unlock the phone without a passcode.
Oh, and it comes in gold!
The phones have the same size screen, a nearly identical metal enclosure, and are extraordinarily similar otherwise. Both will run the new iOS 7 just fine, including features like AirDrop.
Camera: Better low-light performance thanks to a larger sensor with bigger individual pixels and a faster (wider aperture) lens. The dual LED flash should allow for better performance and truer fleshtones as it adapts to room light and color (really!). The ability to shoot a burst of 10 or more images quickly and to shoot slow-motion video also appear to be unique to the iPhone 5S camera as they are not available on the 5C, which shares most hardware with the current iPhone 5.
The burst mode is intriguing in that it allows you to either keep many images or will automagically select the best image of the lot based on sharpness and whatever else it's using. The 5S camera can also shoot slow-motion video at 720, 120 fps and the camera includes image stabilization technology.
Battery: Some tweaks to the insides of the iPhone allow for a slightly larger battery and Apple quotes some numbers that suggest a slight (very slight probably) improvement in battery life. Sometimes, this is one Apple lowballs and reviewers find Apple does better than specified. But don't expect any miracles here.
Processor: The new A7 chip is 64-bit and should be a bit faster, especially for games that are optimized to take advantage of it. Whether you notice this difference on a day-to-day basis is another matter entirely. Many probably would not.
Fitness tracking: If you get a 5S, it will have the ability to act like a Fitbit or Nike Fuel with the right apps, since Apple built in sophisticated motion tracking hardware. Whether you'll want to carry it around like a Fitbit is another matter, of course.
Fingerprint sensor: If you need to protect your phone with a passcode, you might appreciate the fact you can now use your fingerprint instead. The Home button has a sensor that will detect it and unlock the phone for you automatically (once trained to recognize you) when you place your finger on it. It can learn multiple fingers (think spouse or kid) but has some nice features like "allow your kid to unlock the phone to play Candy Crush but not use iTunes to buy extra lives." Oh, yes, the fingerprint can replace your App Store/iTunes password. It can't replace other passwords at this time, though.
Conclusions: Like its predecessor, the 5S costs $199, $299, or $399 depending on whether you get 16, 32, or 64GB of memory. The 5 will be discontinued in favor of the 5c, which has the same hardware in a plastic colorful shell.More questions on Apple September 2013 iPhone Press Event: