we upgraded from Outlook 2010 to 2013 x64it and the exchange server is the same 2010
when trying to cleanup public folders the Clean Up tool is grayed our and it says "outlook 2013 this feature is not available because you are running in online mode and connected to microsoft exchange server 2007 or earlier" none of this is true.
It works fine when you are in your own inbox, only grays out in Public folders, this worked fine with Outlook 2010
David