I have posted before that Fred's numbers don't match mine at all. I don't know what is the situation there. Perhaps he is using 1990s equipment and I have newer switch- mode equipment, no idea.
Eg with a 1000w PSW inverter (although I don't think the PSW vs MSW matters in this case), I can run a CFL bulb in a 120v lamp that draws a total of 1 amp DC as seen on the Trimetric. It throws more light than a regular 12v double lamp that draws 3 amps DC.
I do see a bigger draw using the 2000w inverter to run the same thing as the 1000w inverter, but not much. It has to do with the inverter's efficiency curve where you compare the actual load vs the max inverter watts. Best efficiency is just over half the inverter rating. It hurts more if you run a 190w load on a 200w inverter than it would on a 300w inverter.
That is often confused with the "stand-by draw" of an inverter with no load. Not the same thing at all. You don't add the stand-by draw to the load draw for some kind of total. Lots of people on here seem to think that is the case.