Futuremark:

Our benchmarking data shows that, rather than intentionally degrading the performance of older models, Apple actually does a good job of supporting its older devices with regular updates that maintain a consistent level of performance across iOS versions.

That said, there are some factors that might affect people’s perception of performance after updating an older device with a newer version of iOS. An update might add new features that use more resources or require more processing power. New apps developed for the latest models might not run as smoothly on older devices. Conversely, apps designed for an earlier version of iOS might not take full advantage of optimizations in the latest version. And then there is always the  psychological effect of knowing that there is a new and improved model available, which can make your own device seem outdated.

Myth busted.