I use Win7 and XP on this PC and what little I do use Win7 (I still hate it) I have never noticed any difference in FF of either windows versions.
One thing I would always recommend though with FF is to use the Sync option as it will automatically keep all your favourites and passwords up-to-date on any PC that you have or even use.
Setup Sync on the one version, copy your Sync number to the PC, start your other version of Windows then start and paste your Sync number in the Sync box, from then on .................... simples.
Sorry for going OT.