There was a problem of this kind with Office 2010, for which a hotfix & registry edit were required. See:
http://support.microsoft.com/kb/2504009. I'm not sure if it's the same issue for Office 2013 - I doubt you could use the Office 2010 hotfix and the path for the registry edit would differ too.
Another possibility is that Word 2013 is slower working with Office 2007 files than with native Office 2013 files.