They use the same batteries as everybody else. What is different are more high-performances CPUs which require every bit of power the battery can provide to perform at optimum. The issues as described by Apple and other places like iMore is that at times of high load, the CPU will slow down temporarily, i.e. be throttled, to avoid shutdowns associated with the aged battery being unable to provide peak power anymore. When the load goes down, the CPU goes back to normal. That is a completely reasonable solution to a problem. The problem is that they didn't mention that in the release notes, and so people assume the worst intents. Paranoia has it's day.
As an iPhone 6s user who saw some battery issues, including 2 sudden shutdowns as the battery seemed to drain suddenly, I am glad they provided a fix which made my phone stable and useful again; the alternative would have been that I would have had to get a new 2ndhand phone, or simply replaced the battery. This way, my phone's useful life is extended. Sometime this year, perhaps in a few months, I will take advantage of the battery offer. There is no rush for me, and no point swapping batteries that still work fine, even if not at optimum.
My wife is on an iPhone 5, it is getting long in the tooth (it's from 2012), and she'd like a better camera. So I'm gonna find a 2ndhand 6s off eBay, and at some point will get its battery replaced too if it needs it. Seriously, what Android phone would last you with full OS and software support for 5 years? With a Google phone, like a Nexus or Pixel, a maximum of 2 years; with any other Android phone, like Samsung, a year if you're lucky, with months between the release of critical security updates from Google until it reaches your phone with all the vendor tweaks. That is planned obsolescence, as without OS updates, it leaves you exposed to malware like Stagefright.