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.