Based on the change log for version 2.16, the processing tools in the vector menu have been replaced with the processing algorithms, they have been purposefully removed. This was the removal of the fTools plugin. http://changelog.qgis.org/en/qgis/version/2.16.0/

I had the same issue, first thought it was intentional, but discovered if you delete the .qgis2 directory from user account this fixes the problem. See https://hub.qgis.org/issues/15265