You missed the point, battery capacity has little effect, its the current driving the lens motor, and that is based on the voltage and resistance using ohm's law E=IR.*UPDATE 2*
The battery does help a camera body autofocus an EF lens faster.
From Chuck Westfall… “In addition, the EOS-1D X achieves a higher lens motor drive speed with select L-series USM telephoto lenses than the 5D Mark III because of the 1D X’s more powerful battery pack.”
Exactly, power, i.e. V x A = W.
1 x LP-E4N is 11.1 V x 2450 mAh = 27.195 W
2 x LP-E6 is 7.2 V x 1600 mAh x 2 = 23.040 W
27 W vs. 23 W, not much of a difference, but it's there.
Given the same internal resistance of the lens motor, the current would be about 11.1/7.2 times larger or 1.52 times as much current going thru the motor. Presumably the internal resistance of the bigger battery is lower, so it would have little effect.
That will drive the motor much faster.
You are confusing power and energy.
How am I confusing it??
We are talking about autofocus speed of a lens, and the fact that a higher voltage drives the motor faster. The higher voltage generates more current in the motor which generates more torque and rotates or moves it faster.
Battery capacity does not move a motor faster.