This comes up every once in a while.
Basically, there's not a 100% true rule, since
devices vary. The battery outputs it's voltage the same way...say 3.7 volts...but the amp draw varies. Actually, the voltage starts at 4.2 and drops from there, but never mind that now. So the voltage circuits "boost" the voltage. And depending on the design, the efficiency can vary.
For stacked battery devices (research this 1st, don't just go stacking
batteries...it's dangerous) they only "buck" the voltage...cut it down. I use a VV box mod that takes two
batteries in series for that reason, and it has a switching regulator that's pretty efficient.
So basically, to get more volts, boosters draw more amps. You don't get something for nothing.
In the end, it's really about the watts you use. And that is affected by the ohms of the coil as well as the voltage. Research "ohms law" and such. Basically, watts = voltage squared divided by ohms. So...watts = V
2/Ω. The more you use, the faster it will discharge.
That's a total over simplification, but gets you in the ballpark. For example, some regulators are more efficient at higher voltages. Others seem to find lower voltage lasts longer with their devices. Sigh. But a guarantee is that more watts = faster use than less watts.