Well, obvious to say, but it really depends.
5S has fast 4G LTE speeds for network data. 4S has still decent network data speeds, but not LTE quality. It depends on your area of coverage. Some 3G speeds can be as fast as LTE speeds in certain geographic areas.
For me upgrading from the iPhone 4 to the iPhone 5 last year was a HUGE upgrade. Actually, the 4S has a better 3G network card than the iPhone 4, allowing for noticeably better speeds!
For me, living in Orange County, CA, the difference from 3G to 4G LTE was akin to waiting 30-40 seconds waiting for websites to download on Safari with 3G, in comparison to now 3-6 seconds on 4G LTE. I have AT&T by the way. The 4G LTE is nearly as fast as our home Wi-Fi speeds, which are maybe 25-30 Mbps.
If you care about data, and your ability to always be connected, then the 5S is your best choice. Just watch out for your data usage, since all the latest smartphones are "data hungry" more so than ever.
Go for the 4S if you want to save money, don't mind the smaller screen at 3.5" vs the iPhone 5S's 4" screen. The 1/2" really adds a lot! The iPhone 4S is starting to show its age naturally, being released in Fall 2011.
4S also has Siri, the voice assistant.
Go for the iPhone 5S, Apple's latest, if you would like the lightest, and thinnest Apple mobile device yet. Does security matter to you? I hear the Touch ID for the iPhone 5S home button works great! I have yet to try it myself.
You can essentially use your finger to access your iPhone 5S every time you use it, waking it from standby and using your iPhone, without having to set a password. Optional feature of course. But, a nice future-thinking touch by Apple, making it a modern feature that all smartphones will now strive to be like.
Definitely get the iPhone 5S instead of the 5C, for the extra $100. I know you didn't mention the 5C, but the 5S is considerably better in every aspect.
Have fun choosing a smartphone. I always have lots of fun comparing all aspects of phones to see what I need and suits me the best.
Cheerio.