Depends on the device! Even for just one particular device.....
For example:
Variable Voltage Box Mod
This box mod dissipates the
voltage difference between input voltage (stacked batteries) and the desired output voltage setting AS HEAT (wasted energy). The lower the voltage, the more inefficient it is the worse the battery longevity. So it will give better battery life at higher voltages as it's closer to native voltage,
amp draw goes down as voltage goes up. Thus, you'll get better use of the battery charge at higher voltages....which is his question.
This is verifiable by real-world experience, BTW.
Think of it this way... the internal electronics act like another atomizer coil (a "black box" that eats some power) that is not being applied to vaping. The output side of his equation is constant power...BUT THE INPUT VARIES depending on efficiency of that "extra stuff black box". Of course, the input is the battery drain.
The efficiency of this device varies depending on voltage output setting.
EDIT: That's not a slam to this mod....I have one (well, I built the kit) and use it all the time. And I know it varies. I deliberately use higher ohm/voltage stuff when I can to max battery life.
OTOH, for other devices, I've seen several users swear that for the same watts, lower voltage and LR stuff lasts longer (I can't verify that one). eGo twist seems to be indicated to do this. IDK why, but that's the rumor.
Thus, the discussion degrades into device design when we begin discussing the answer...because it depends.
There may very well be some devices that ARE about the same at varying voltages constant watts.