Generator power factor for charging batteries

The alternator on diesel generators can be specced as .8 or 1 power factor. In a scenario where the generator will be used to charge batteries (via a charger), which power factor is better?

I believe if the driven device has poor power factor you want the .8 as that should compensate for the additional apparent power needed.

https://woodstockpower.com/power-calculator/

Verify with the supplier what you will be driving with the generator.

Xantrex white paper on power factor

So in a scenario with a pfc enabled charger, the leading or lagging nature of the current becomes irrelevant because the charger will correct and sync with the current. That makes sense. So the more efficient pf 1 would make the most sense for a home standby generator.

I did not know if the charger itself while operating was considered a capacitive or inductive load.

Home standby generator could be running an air conditioner, microwave, fridge, well pump besides the charging system to replenish a battery.
Electric oven is easy but an inductive cooktop I don't know.