MissBlossom
Work/energy is total output over an extended period of time. Power is instantaneous output, but they are closely related. Basically, you could say that power is how hard it works, time is how long it works. In the end, how much it works depends on both.
MissBlossom And since Watt-hours = Watts x hours = volts x amps x hours, I don't see how it's possible that "Voltage has nothing to do with the energy content of a battery."
Most batteries stay at a relatively stable voltage over most of their useful life, so while measuring the voltage can tell you how full a battery is, there is a very indirect relation between the voltage of the battery and how much juice there still is in it. If it goes significantly below the nominal 3.6 V, it is empty, if it is much higher than that, it is full to the brim, but outside of those extremes it will stay at around 3.6 V for a loooong time.
Voltage absolutely has an effect on how much work you can do (per time) with a given amount of amps (which is why those big transmission lines that go between cities run at hundreds of thousands of volts), But when you compare similar batteries, the voltage is practically the same between both, so using Amp-hours is enough for comparing their juice.