That was my thinking as well but this is a metal capable device, meaning all the UI should be drawn on hardware and should be fast. So either Metal needs additional memory to operate efficiently, IOS 9 requires more memory or a combination of factors is at play here.
Why would it need more memory? According to Anandtech, the devices don't run out of memory when the stuttering occurs, so it's related to bad coding in relation to the use of Metal.