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I own both a P2D and a L2D and right off the bat I will suggest that the difference in current draw is simply voltage. You mistook the term "power" for "current". I'm a retired electrical engineer and often non-electrical people will confuse voltage, current and power. All three are linearly related. The P2D uses 2 CR123s and the L2D uses 2 AA batteries. Assuming ideal conditions that an AA is 1.5 volt and the CR123 is 3.0 volt, to drawn the same power from a CR123 you need only half as much current. Power is measured in Watts and the equation is P=VI where Power=Voltage X Current. You can deliver more power by either increasing the current or the voltage. But higher voltage is much more efficient. That is why power companies transport power at very high voltage. You can deliver for example 1 million watts across transmission lines at 1amp X 1 million volts or you can TRY to transmit the same at 1000 amps at 1000 volts. A 1000 amp current will have much higher transmission losses then 1 amp. The voltage drop loss will be the resistance in the transmission lines time (x) the current. So that if the transmission line has a resistance of ½ ohm, the voltage drop across the transmission line is 500 volts for a 1000 amp load or ½ volt for a 1-amp load. I don't want to stray too off topic, but generally higher voltage is better and more efficient. However once you get to 80 volts and higher there are concerns of safety, and extremely large voltage, there is the danger of dielectric failures and arching.
