Yup, no "one correct answer" to this one.
If you leave it on, if you are not on shore power or generator, anything on any of the circuits fed by the inverter will begin drawing from the batteries. Good if you happen to be watching TV. REALLY BAD if you have a space heater plugged into one of those outlets as it could ruin a very expensive battery bank if shore power goes out.
And when no shore power or generator, even if there is nothing operating, the inverter takes a small amount of power in "stand-by mode". So, when storing where no power, be sure to turn it off.
In general I only leave it on when I want it to use my battery power to run 120 VAC appliances.