Autodesk have a stand alone FBX converter which takes dae, fbx obj and few other formats and allows you to convert them to various generations of fbx formats. It's available here, about half way down the page:
http://usa.autodesk.com/adsk/servlet/pc/item?siteID=123112&id=10775855 for Windows and Mac. Unfortunately none for 'nix boxes. I have had a lot of trouble with the various versions of dae and fbx formats, and this tool seems to be able to do 'robust' conversions, better than the importers/exporters in max.