You need to right-click on a file or folder, select "properties", and click the "Security" tab. Inside the resulting dialogue box, clicking on one of the group or user names will show the access that it has in the lower pane.
What you're looking for is the groups that have "full control" access. If a generic group such as "Administrators" or "Users" (but not "SYSTEM") has full control access, then you'll be able to access it with the equivalent generic group on the 64-bit Windows system. But if the only names to have full control access are accounts for specific users (JoeSmith, for example) then the 64-bit system will be denied access.
Unless you've customized the access to subfolders, you can generally just need to do this for the top-level folder. The default is for all of the file and subfolders within to have the same permissions.
Don't sweat it too much if you're not sure. Even if you're denied access under 64-bit Windows you can still get around the problem by taking ownership of the files/folders and then changing their permissions.