Where did I say anything about torque in my reply?
So, if your control linkages are binding and stalling your servos near the endpoints of travel, you are going to get shorter battery times with six volts. If everything moves freely, your battery life should not be that much different.
That happens with 4.8 volt batteries too. 'Load' doesn't care what voltage the batteries are. Load equals current draw and power depletion, power being voltage and current. If there is a bind, it just doesn't matter what the batteries are, they will deplete faster than if there was no binding.
CGr