Same idea here. I did find that the idle draw on 400w to 1000w was about the same small amount but that the 2000w did have more. I have remote on/off switches for both inverters (a 1000w PSW and a 2000w MSW) and leave them off when not running something 120v.
I have a third inverter 150w MSW that plugs into the Winegard 12v socket that I use for odd jobs like the set of 2.1 powered speakers.
It's not the idle draw that matters when you leave them turned off anyway, but it is the extra amps draw the big one uses on small loads that counts. The inverter efficiency curve is max around 3/4 of its wattage and gets poor at low and high in its wattage range.
That means you draw fewer amps running a 100w TV/dvd with a 200w inverter than with a 2000w inverter, even though the 120v wattage load is the same. Can be as much as 2 amps difference.
It is useful to have one of your inverters be PSW in case you have any loads that must have PSW instead of MSW. Most stuff runs on MSW ok.