As David suggested, both computers should have the same version for you to be able to use the catalog from one computer on the other. During a version upgrade, like from version 8.x to version 9.x the catalog is upgraded to be comptible with the latest version. The upgraded catalog is then compatible only with the latest version and not with the previous ones.
You can however use the old catalog. During the catalog up upgrade, a copy of your catalog is created and the copy is then upgraded to be compatible with the latest version. So if you still have the old version of the catalog on the Mac, you can move that over to the Windows PC and use that on it. It would not have your latest edits or the images you have added in version 9.x though.