That doesnt answer his question.This is the first release of the beta and the OS will be laggy and buggy on all devices, not just the iP4.
You will have to wait until the final release when they will smooth out everything. It will probably be a tad slower than 4S/5, but still snappy.
I installed it on an old 4 to test. Hard to tell how well it will work as I can't even get 1 app to install and it keeps rebooting.Has anyone installed iOS7 on an iPhone 4? If so, how is the performance on it? I ask because the last release for the 3GS made it very slow and was curious if iOS7 slows down the iPhone 4 substantially.