Considering your degree, I would assume your working knowledge is greater than mine, but ignoring losses due to heat seems like it wrecks the analysis.
Energy loss due to heat is energy that isn't doing work, and higher amperage is what causes that heat loss. So with higher voltage, you can use less amperage, which means less energy loss due to heat, which means more of that energy is going towards doing work. To me, it's not about a bigger tank, it's about not having a fuel leak.
All that is to say that higher voltage tools can push themselves harder without hemorrhaging power. But again, I defer to your expertise.