IF all else was equal, I would agree with most of Nick's and Bill's comments, but I doubt all else is equal between the Rigid and Panasonic tools being compared. If the same battery, electronic control circuit and motor technologies were being used, then I would agree that a higher battery voltage will produce a higher torque output of the drill motor.
It appears to me that our knowledge level would benefit if someone who really knows various battery technologies and portable tool motor technologies would join this thread and give us a detailed explanation. I suspect the Comparison of the performance of a Rigid 18V drill with 2.5AH battery to a Panasonic 15.6V drill with a 3.5AH battery lacks enough details to be a comparison of the batteries; it may be more a comparison of the design of their motors, gear trains and control circuits. The AH rating of a battery denotes the total amount of energy that it can hold [and presumably later deliver] when fully charged. That AH number alone doesn't tell you how rapidly it can deliver that energy to run a motor of a tool; i.e. the power output capability of the battery. Nor does the voltage, because that output voltage may rapidly fall as more current output is demanded by the control circuit/motor. The power delivered W (watts) may be expressed as V (volts) times A (amperes). What are the dynamic V x A characteristics of the various batteries under consideration? We don't really know. Have you ever noticed if you run down the battery on a tool, then leave it sit for a few minutes, then try it again, it may give you a very short burst of power. That is due to the voltage climbing back up during the rest period, but that voltage falls off very quickly when the battery is asked to deliver a lot of current when you try to run the tool again. The same phenomenon often occurs when the battery in your car is nearly dead; the headlights and horn may work OK, but the battery can no longer deliver the sufficient amperage at sufficient voltage to crank the engine. The same phenomenon occurs whenever you get/give a static discharge, except that is a capacitor being discharged rather than a battery.
It is also possible to utilize electronic circuitry, transformers and such, to step up the voltage from the battery to whatever is needed to run the equipment. In my previous employment, I worked with designers of the electric braking systems now being deployed on aircraft. These systems run supply voltages as high as 280V, but the [lead acid] batteries are not above 28V. Even when running only on battery power, these aircraft systems can overdrive the motors if needed in an emergency situation, producing a brake torque higher than their hydraulic counterparts, three motors can be made to do the work of four for a short time (longer periods would overheat the motors to self-destruction). It's all in the design of the system, not the inherent characteristics of the batteries. Where very large amperages are needed for short periods of time, capacitors are often used to supplement the power available from other sources.
Festool's (and some Panasonic) C12 and newer model drills use 3-phase motors which are much more efficient and provide much more torque for a given size and weight than their single phase DC counterparts found in most other drill and other battery-powered tool motors. These tools have internal circuitry to create the 3-phase current used to drive their motors.
Dave R.
