Sorry this is a few posts late but....
I run two hub-geared bikes, one with a very old K-series (pre AW) 3-speed (less obvious neutral than AW's), and another with a Nexus 7 of dubious history. Both also have hub brakes. The bikes are very different BUT the Sturmey is DEFINITELY giving less drivetrain friction, in all gears. Other Sturmeys' I've known were similar. This goes through an enclosed 48/20 geartrain with 26x13/8th wheels.
The Nexus is driven through geartrain of 33/16 on fat 700c's giving a middle/normal of about 56", so it runs with no. 5 (about 65") as main road gear. I want to drop the gearing to 42/21 to give a slightly lower range and better chain wear/efficiency. Even the middle (no. 4), gear is NOT direct drive, Shimano state it's 0.989 from direct , so it's running through some transmission even there. Nexus has lower friction on gear no. 6 (about 75") but is very draggy in all other gears. Might have been poorly maintained, I dis-assembled and gave it a dunking in gear oil 2 years ago which helped but it's never been great - other than you can easily get a decent gearing spread from 35"-85" a la
Velocio with even steps and no neutral spaces. Even allowing different drivetrain details the Nexus drags noticeably.
Sturmey 3 AW's (and this K), are like hitting a wall with your kneecap when you change up. Efficiency is good but the spread is really wide (is 3 ratios really a "range" of gears?!) - but when will the AM and AC's reappear?
my 2 pen'orth