Watt-hour vs Amp-hour - Battery life
Watt hours is the amount of energy the battery can deliver. Ampere hours is the amount of charge it can deliver. Which of those maps better to your load run time depends on the type of load.
If you have a load capable of using all of the energy efficiently, that is, your load starts with a good switchmode power supply, then the time it can run will be governed by the Watt hours. A switchmode regulator can deliver a higher current than it receives if it is regulating the voltage down, so the total charge in the battery does not relate to the run time.
If on the other hand you have an inefficient linear regulator that wastes energy, while it outputs essentially the same current as it receives, then the battery Ampere hours is more useful. As the battery voltage varies, the regulator will waste variable power, but the run time will still be governed by the charge.
If you have a low voltage load, and a high voltage battery, then running the load from a switch mode power supply will get you significantly higher load run time than running it from a linear regulator.
If your load draws large peaks, and then sleeps for a long time, you may need to choose your switch mode power supply carefully, so that its quiescent current doesn't dominate your load's sleep current. Designing for and verifying load life in such circumstances is non-trivial.