AFAIK neither the Sturmey 8 nor any of the many Shimano 8 variants have been empirically tested for efficiency. Because of the way the Sturmey creates its ratios, some have theorized it is relatively efficient, but real world efficiency depends as much on small details of construction as general design. The ten different Nexus/Alfine 8-speed models released by Shimano to-date certainly have different efficiencies.

I'm always amused that cyclists fuss over the efficiency of IGHs but never raise a peep about efficiency in derailleur gear drivetrains (and yes, it can vary quite a bit!)

Best,
tcs