OK, I see where you were going. So:
power (rate of energy discharge) = voltage x current (amperage)
energy = heat + work = power x time
[I.e., using SI units, power is measured in watts, and work and heat are forms of energy, i.e., of power x time, so work is actually watts x seconds = joules, which can be converted to BTU or any other unit of energy.]
Heat and work are both flows of energy from a system to the surroundings (what we define as the system is arbitrary, and here it makes sense to initially define it as the battery). Now here it gets a bit tricky with the thermodynamics and the strict definitions of heat and work flow and system vs. surroundings (heat and work are only defined when there is a flow of energy across a system boundary), but I'm going to ignore the rigor for the purposes of simplicity.
So in this case, we can say that the battery does work on the surroundings by making electrons move through a resistive element, and that this work is entirely converted to heat:
energy = electrochemical work done by battery = (via 'resistive conversion') heat flow into foot & boot = power x time
power = rate at which work flows out of the system = rate of heat flow into foot & boot
[I'm ignoring the possibility that something in the heating element is converted to a higher potential energy state by the flow of electrons, and that it remains at this higher state, since that would be work that was not converted to heat.]
So let's first consider work: If we assume both batteries can discharge all of their capacity during a ski day (set on high), the 2000 mAh battery can do 2/3 more work (creating 2/3 more heat flow into the surroundings, i.e., the foot & boot) than the 1200 mAh battery. This would be independent of voltage (unless voltage has some effect on %discharge).
Now let's consider maximum power (= max rate of work flow = max rate at which heat can flow into the foot & boot). That's max. (voltage x current). Here the voltage would of course be relevant, but not by itself; what counts is the maximum of (voltage x current). This is probably dictated by the battery technology along with whatever regulation circuitry is used.
Hope there are no typos, since in a few minutes I won't be able to edit this!