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Logically Windows 7 Professional should be slower than Windows 7 Home Premium because it has more features to take up system resources. However, one might expect someone spending more on an operating system to spend more on hardware so that you can reach a neutral situation as Ben suggests. In practice there are many other factors which can determine system performance.
The choice of hardware is likely to have a bigger influence on performance than the selection of one version of the operating system over another. Choice of security software can make a noticeable difference. System maintenance and avoiding unnecessary software are other factors.
If all other things are equal one user can have a lively computer whereas another user will find the same computer sluggish. Some users misuse their computer, ignore errors, and fail to carry out regular housekeeping.
Hope this helps, Gerry Cornell