One thing about MSW is it does not pull as many amps from the battery when on MW duty. The 1500w input on PSW is more like 1100w on MSW and that shows up in slower heating.
I calculated that you draw fewer AH using the MW on MSW than with PSW to do the same job. The time is longer but the amps lower (110a vs 150a say) so Peukert makes it a better deal to have the MSW. Also 110a means not hitting that 11v alarm so soon as with 150a too, if you have a smaller battery bank so that matters.
Problem is some MWs don't work well with MSW inverters and there is little info on which ones will with which. However many folks report theirs works ok.