Hi,
My Cobra draws 0.5 amps at idle. Some high end inverters "go to sleep" and draw only one or two watts. Inverters, when in use, are inherently not likely to be more than about 90% efficient. PSW are less efficient in general than MSW units.
I tend to switch off my inverter when I'm not inside in the summer time. In the winter that's a different story as I power several devices to prevent freezing.