I'm Just Hazarding a Guess But......
I've seen programs that specified they were for XP Media Center Edition, but none which specified XP Home versus XP Pro.
I'm not completely familiar with Vista Versions, so I'm not sure if Vista Business contains the Media Center features that Vista Home Premium does. I do know that Vista Ultimate contains all features of all other versions.
So, here's the guess, if the program has to do with media center functions, and Vista Business doesn't have them, there could be a problem. Other than that you're probably god to go. (still a guess).
Well another issue could be as a server host. XP Pro would do this, XP Home, no.
My understanding is that even Vista Basic should be able to run all apps intended for Vista, it simply lacks the "Aero" interface.