B.L.E.

Going to six volts means that your servos can make more torque, it doesn't mean that they will make more torque. The torque a servo makes is exactly the amount needed to overcome aerodynamic forces, hinge friction, and linkage friction. Since that doesn't change when you go to six volts, neither does the torque the servos need to make. The unloaded amp draw of a permanent magnet DC motor is nearly constant with changing voltage.

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.