Like many others, I experienced the problem with the 8.4.19 (8/16/2016) build of Dropbox. In my case, Revit® 2014 would display the whirlpool of death when selecting Open > Project from the Application Menu or selecting the Open link under Projects in the Recent Files window. I did not have any problems with AutoCAD®.
I just forced the current build of Dropbox to install (8.4.21), and I no longer have that issue.
For the record, here are the Autodesk Knowledge Network articles related to this issue:
AutoCAD becomes unresponsive when opening or saving files
Revit: Hang when clicking Open after recent Dropbox update