I have always thought that English gun makers had the best idea as to "turn screw" tips. The tips were made to fit a certain size screw. The tips were ground with a radius so the tip rested on the bottom of the screw slot. That is where the pressure is applied when force is exerted turning the screw.
This resulted in less slippage and way less buggered screw heads.

Sorry for the size of the pic. I reduced it as much as I could.

Ed,

Your spot on there. Here is a tool I use to shape the drivers to prevent maring the screw heads.

close up of tip after

That is a neat sharpening jig Chris. Manual operated, for more control. Holds drive at a 90 degree angle, changeable collett holder.

Do all watchmakers sharpen for a radius?

I don’t think they are commonly used. I invest heavily in upgrading my tools & equipment. Next month I am trying to arrange for the re calibration of my timing machine by the manufacturers, and following month I have my eyes on a top of the range case back machine, and so on my list is endless I love nice tools.