The standard science for this starts on page three
here (pdf).
As mechanical devices, broken in and properly lubricated three speed hubs are the most efficient poly-speed bicycle drivetrains across all their gears. However, human muscles also operate on a efficiency/speed curve, and the large gear steps of a three speed drivetrain drive the overall machine+human efficiency down.
Derailleur drive trains have some interesting inefficiencies, most of which are unknown to cyclists even in 2016.
Really interesting, thanks. I'd always been sceptical of the "derailleurs are more efficient" assertions but had no idea of the facts.