I noticed this post today from Brad Teed…It's a good one!:
I would have assumed that the content types would be the same in either mode, but evidentially not! There is a check in the code at Microsoft.SharePoint.Taxonomy.ContentTypeSync.Internal.PackageInfo.ValidatePackageVersion(). It checks the hub site collection compatibility level and then checks the current web's site collection compatibility level. If it doesn't match, then it errors out. This is a bummer for those that used the Content Publishing Hub in 2010 and must now upgrade all site collections at the same time to "15" in order to get updates from the hub.
However, there is something else interesting here. The APIs that are being used by the content type hub publishing are the Content Deployment APIs. So the package that it is checking is a simple export/import package that you would do with anything else. The thing that jumps out at me, that I would have assumed one could do, is export from 2010 and import into 2013 using those APIS, but it look like that is not a good path to take being that they specifically are denying you from doing this. This tells me that you should upgrade your older sites to 2013, then do an export, then do an import into 2013.