I suspect on bigger pots with bigger exchanger the result would be closer [to Primus' claimed efficiency numbers].
Not sure. Interesting question though. Generally, a wider pot is more efficient at heat transfer than a taller pot. But if you widen both pots equally, would the pot with the heat exchanger pull out ahead in terms of efficiency? I'm not sure that it would.
I definitely would take a wide pot with a heat exchanger over a narrow pot without one.

HJ
Since its all about surface area I would take a pot with a potskirt

prefering a pot that is slightly taller than it is wide
( SA( 478.5) d(10.0) h( 12.7) v(1.0) )
surface area of a pot available for heat gain
bottom + sides
pi*(r^2) + 2*pi*r*h
SA(cm^2) d( cm) h( cm) v(liter)
SA(2003.1) d( 2.0) h(318.3) v(1.0) -- pipe
SA(1012.6) d( 4.0) h( 79.6) v(1.0) -- pipe
SA( 694.9) d( 6.0) h( 35.4) v(1.0) -- pipe
SA( 550.3) d( 8.0) h( 19.9) v(1.0) -- pipe
SA( 514.2) d(20.0) h( 3.2) v(1.0) -- skillet
SA( 478.5) d(10.0) h( 12.7) v(1.0) -- pot
SA( 476.7) d(18.0) h( 3.9) v(1.0) -- skillet
SA( 451.1) d(16.0) h( 5.0) v(1.0)
SA( 446.4) d(12.0) h( 8.8) v(1.0)
SA( 439.7) d(14.0) h( 6.5) v(1.0)
New publication for all those interested in efficient stoves
Test Results of Cook Stove PerformanceFour techniques to boil water faster:
1. Create a large enough fire in the combustion chamber.
2. Force the gases to flow against the bottom and sides of the pot in narrow channels.
3. Make sure the gases are as hot as possible.
4. Increase the speed of the hot gases flowing over the surface of the pot.