If the MW will run on MSW but at lower power so taking longer, it is easier on battery capacity than with PSW due to Mr Peukert.
Eg a 1000w will draw 150a on PSW but only 110a on MSW. A potato takes say 9 minutes instead of 7 to "cook".
150 x 7/60 = 17.5 AH
110 x 9/60 = 16.5 AH
If the inverter MW did full power on MSW that would negate the advantage in AH.
This may be fairly trivial in the big picture for those sort of AH numbers, but say you have a 700w MW that wants 1050w and a 1000w inverter.
The PSW 1000 is drawing 100a and showing 1050w with its overload lamp on (but it will run) If it were a 1000w MSW it would be drawing maybe 80a and not being overloaded. You still get to eat your spud but have to wait a minute or two longer.
Looking at it another way, means the MSW 1000w inverter could run a 900w MW but the PSW 1000 could not. Maybe you can get a bigger pot or wider plate to fit in the 900 so that would be the advantage there if so.