I don't want to put it down too much simple but let's try:
where "P" is power,"V" is voltage and "i" is the current. (Units of measure [Watt], [Volt], [Ampere] )
if we keep "i" costant, we have:
11,1 * i > 7,6 * i
e.g. 11,1 V * 1A = 11,1 W > 7,6V * 1A = 7,6 W
The result is that a 11,1V battery can spin the lens motor phisically faster than a 7,6V battery,
if there are no differences in circuits, I mean, amplificantions, cuts, stabilizations etc etc etc, and obviously the lens must be designed to accept a certain range of potentials.
Things are not so simple, but this is only for exemplification purposes.
The stepping motors have a set resistance on the windings. It does not matter which camera or battery you are using.... the resistance stays the same.
The pertanant equation is P=E^2/R, or Power = Voltage times voltage divided by resistance. I don't know what the resistance is, so we can not compute what the power is, but we can calculate the ratio of power using an 11.1 battery against a 7.6 volt battery. We get (11.1*11.1)/(7.6*7.6) or 2.13.
A camera using an 11.1 volt battery has twice the power to drive a lens stepper motor than a camera with a 7.6 volt battery....... but remember that this is only one factor in AF speed.... there is how accurate the af sensor is, how fast the camera's computer can interpet the results, the search algorithm, and probably a dozen other things that I am unaware of. The battery voltage is just one part of a very complex system.
Since the motors are USM, it means they are driven by an AC current rather than DC. (In this case >20kHz.)
Strictly speaking; AC motors/ transducers have an impedance, not a resistance.... An Impedance changes with Load and drive frequency (in this case torque needed to move an element) so the same motor may present a different impedance, there would be other factors like the angle of the load... all this complicates things a bit.
Seems that the Canon USM motors have a good spread of voltage tolerances, this would enable them to use similar motors (volume/ scale efficiencies) in many different lens designs... would also explain why the larger element lens may sometimes perform worse than their smaller brethren perhaps.
It should be fairly easy for Canon to tweak the control circuitry to deliver larger voltages in bodies with larger power supplies to drive some of these lenses AF quicker... more voltage would spin the motor faster (assuming current holds up).
Which begs the question....
Would you wear out a lens motor on a 1 series body; sooner than you would on a smaller body?