The QGIS project site's How Do I Do That in QGIS should be a good starting point.
It is intended to show how to perform basic GIS operations in QGIS in
the most straightforward way. It is modelled after “How do I do that
in ArcGIS/Manifold?: illustrating classic GIS tasks”. That document
illustrated a selection of tasks which were thought to be
representative of common usage in 2004, and was itself derived from a
checklist of essential GIS functions that was included in 1988 in “A
Process for Selecting Geographic Information Systems”.
You might have a hard time looking for materials that target advanced operations QGIS operations, though. Those usually are part of paid training sessions offered by consulting companies. I think you're better off asking your users what operations they need and then mapping them to the QGIS equivalents, assuming there are any. You can then build your own materials based on those. That way, you'd end up with customized materials that actually meet your users needs.