Actually, they don't. Not anymore. The GPU acceleration that has been in Photoshop since CS4 and all other products since CS5 works better on Windows platform. Also the mouse button... not buttons.
It's pure myth that the OS makes any difference between Windows and Mac versions of any programs in performance or usability. Since both run now on same processor it's easy to see. It all comes down to hardware, and sadly GPU acceleration is something that still does suck in Mac.
Sounds like perfect solution. Have the workplace worry about your work computer and software without worrying about your home computer use.