I've seen batteries quoted here in watt hours and amp hours. I think of a battery as a store of energy and the SI unit energy is joules. Watt hours are merely a non-SI way of expressing joules.

I know there are variables such as voltage variation and a duration of discharge and it's often best to use the unit that is less dependent on assumptions.

My impression is that phone and car batteries (for non-electric cars at least) are usually specified in amp hours.

In the weird world of domestic pv:
Which unit is more common for battery spec?
Which unit is 'better' as a guide to battery capacity?
Which unit would the sales people prefer in order to mislead you?