If you upgrade from the iPhone 5
Take slow-motion video
Use the TouchID sensor to add a level of security to the phone
Take better photographs
Enjoy a much faster iOS
Enjoy the benefit of 64bit apps when they start to appear
Use iOS 10 when it appears
Enjoy a longer battery life
Have more detailed reports in fitness apps (M7 co-processor)
If you upgrade from the iPhone 4S
All of the above
Larger screen with better contrast ratio
Smaller physical size
Film 1080p video
Lighter
Improved front facing camera
Double the RAM
4G LTE
I'm using a 4s right now (my first smartphone), and nothing has been introduced in the 5 or 5s that compels me to upgrade.
If I want to take photos, I use my Leica iiif or Leica M2 and Tri-X.
If I want to scan these photos and process them, I use Photoshop and my Macbook Air (which in terms of processing power and screen real-estate, is the bottom limit, but since I'm switching from scanning to making actual wet prints, I don't feel the need to upgrade).
The 4s screen is clear enough for its purpose; that is, I'm not left saying, "If only it had better contrast ratio or higher resolution."
For whenever I might want a larger screen, I'll go to my laptop, or better yet, my TV---and maybe in the future, my 27-inch computer monitor. Going from 3.5 inches to 4 inches or even 6 inches isn't going to make a difference in terms of watching a movie, for example.
Don't care about making videos; and the camera in the 4s is more than sufficient for snapshots.
If I want to play computer games, the 4s is good enough to keep me entertained on the subway, but for all other applications, I'll use my PlayStation 3 (and actually, I only have one game, a flight simulator thing that would flop on a small screen).
Newer iPhones (6 on up) might actually get larger, which I consider a liability, not bonus. As it stands, I like the size and weight of the 4s.
The 4s is fast enough for what I need, particularly since the main role of my smartphone is, perhaps unbelievably, its ability to serve as a phone. I also use calendar, reminders, and text messaging. I'll also check the weather, certain sports scores, Google, Google maps, and less and less, Facebook. The 4s handles all of this with aplomb. I suspect some earlier iPhone models do so as well.
Granted, 3G is a speed hit, but for any heavy downloading (whatever that might be since I don't download movies or songs; still believe in buying lossless format), I use WiFi.
By the time iOS 10 appears, then maybe I'll upgrade to whatever Apple's US$200 (plus contract) offering is.
Let me make it perfectly clear that I'm expressing my personal preference here, and that I'm NOT making any universal or absolute declarations. Choice is generally good, and if someone believes that there is so much as just one thing on the 5s, such as that fingerprint thing, that justifies its purchase, then fine. For that matter, if someone just likes to collect iPhones or wants to buy 100,000 of them to construct an igloo, that's fine too...it's personal prerogative.
However, while I'm not a power user, I do use computers for more than just email and web search, and in such case, there are ergonomics involved that will always keep me more focused on what a Mac has to offer. Even something simple as a PowerPoint presentation is something I would not want to do on an iPad, let alone a phone. Again, I realize that I'm only speaking for myself here, but I also believe that I'm not exactly alone.
In the future, will the iPhone have enough processing power to serve as a high-end server; maybe. Convergence could occur, using these devices as 'pods' that are placed in a dock attached to larger screens, keyboards, 3D holographic projectors, automaton producing machinery, etc., nothing really new about that potential (PowerBook Duo). Until then, though, if I'm going to get excited about power and video, I'll look to the higher offerings: the desktop/laptop computer.