An amp hr at 12v is 12 watt hrs , an amp hr at 13v is 13 watt hrs
No they are not equal
But more important is the chemical reaction efficiency of the battery
It's related to lead plate thickness and density vs electrolyte
Thick solid plates react more slowly to produce electrical current
A slow low amp draw is very efficient
A higher amp faster draw is less efficient , warmer temps actually speed up reaction and are more efficient until the temp is to high and starts causing battery damage
Porus grid plates expose more surface area aka start batteries, and produce more current faster, but do no recover well from deep discharge, and shed more plate material, and loose capacity