Alongside their letter to customers on the iPhone battery/performance controversy, Apple has released a detailed KnowledgeBase article with a technical overview of what’s going on and why:
When power is pulled from a battery with a higher level of impedance, the battery’s voltage will drop to a greater degree. Electronic components require a minimum voltage to operate. This includes the device’s internal storage, power circuits, and the battery itself. The power management system determines the capability of the battery to supply this power, and manages the loads in order to maintain operations. When the operations can no longer be supported with the full capabilities of the power management system, the system will perform a shutdown to preserve these electronic components. While this shutdown is intentional from the device perspective, it may be unexpected by the user.
I love that “may be”.
With a low battery state of charge, a higher chemical age, or colder temperatures, users are more likely to experience unexpected shutdowns. In extreme cases, shutdowns can occur more frequently, thereby rendering the device unreliable or unusable. iOS 10.2.1 (Released January 2017) includes updates for previous models of iPhone to prevent them from unexpectedly shutting down. This includes a feature for iPhone 6, iPhone 6 Plus, iPhone 6s, iPhone 6s Plus, and iPhone SE to dynamically manage the instantaneous performance peaks, only when needed, to prevent the device from unexpectedly shutting down. This capability was also extended to iPhone 7 and iPhone 7 Plus with iOS 11.2, and we will continue improving our power management feature in the future. This feature’s only intent is to prevent unexpected shutdowns so that the iPhone can still be used.
If you have an eligible iPhone (iPhone 6 or later), Apple’s upcoming $29 replacement program might be some of the best money you can spend. But again, if you have an iPhone that is really slow all the time, there’s a good chance there’s something wrong with it other than (or in addition to) the battery. A wipe and restore won’t cost you anything but some time, and seems to solve many “slow iPhone” problems.