This goes for those who believe in conspiracy theories and that Apple deliberately launches software updates that make old phones much slower so that people want to buy newer devices.
Geoffrey A. Fowle, technology columnist for Wall Street Journal and who also believed in this theory, installed iOS 9 (probably the version Golden Master) on four models of iPhones (4s, 5, 5s and 6) and performed four comparative tests: boot (turn on the device), open the Safari app, open the Camera app and view the last photo taken by the Camera app. Each of these tests was done three times on all devices, running both iOS 8.4.1 and iOS 9.
Despite having new features and being a more advanced system (which requires better hardware to run at full steam), iOS 9 performed the tasks practically at the same time as iOS 8.4.1. Below, the graph focused on the boot:
Even having access to a good part of the new features when updating an old iPhone to iOS 9, the system performance is the same as iOS 8 or very little worse (in some cases, fractions of a second); on the other hand, in some tasks such as viewing the last photo taken by the Cmera app, the new system is even faster.
That is, there is no reason for you not to update your iPhone to iOS 9 when it is released today.
(via Patently Apple)