XP

It's common knowledge, that larger companies always want you to replace your older products with the newest ones. There have even been theories that in the case of Apple products, newer software updates actually slow down older products. In France, Apple has already been fined 25 million euros for deliberately slowing down older devices. As stated, Apple "committed the crime of deceptive commercial practice by omission."

Phone batteries deteriorate over time, which can eventually lead to performance issues and crashes. To deal with problem, the software was designed to limit the phones capabilities the further the battery deteriorated. That's the excuses that Apple chose to go with which is somewhat true. However they definitely limit the older phones more than necessary, just to be on the safe side and at the same time force users to buy a new phone.

If you've got an older iPhone that seems to run a lot slower than it used to, I'd suggest just replacing the battery. If what Apple reported is true, that should fix the problem. There are enough tutorials online for all the available models.