onboard kilowatt-hour meters question

[madderscience]

So if both original scenarios can be correct, what do most watt hour meters do to calculate KWH used?  sample voltage and current, or just current?

Given that a certain amount of KWH are stored in a battery, If voltage sag were primarily due to internal battery resistance, you could probably get an accurate reading of watt hours used with a preconfigured nominal battery voltage.  If voltage sag were due to the chemical reaction in the batteries only being able to progress at a certain rate (so the voltage drop is not due to wasted energy, just a limitation on how fast it can be removed from the batteries) then the more accurate reading would be to sample volts and amps.   I suppose it is in fact a combination of the above factors so the safest thing to do would be to sample voltage and current.