Update,we have used the induction burners for 6 days and here is what I've discovered;
Shore power===no problems full power to both cooktops 20amp, 30 amp, or 50amp. One may want to use caution about other circuits being used if not on full 50 amp shore power.
Generator===no problems full power to both cooktops no loss still can boil an inch of water in pan @2min
Inverter===only one burner powers on and it seems to burn the batteries up fast but could still be used for a grilled cheese sandwich i guess. I don't think we will plan on using the cooktop on the inverter unless it is an emergency. This may not fit some lifestyles but does us no harm.
One of the circuits does not power on when inverter is used but that is just as well. I wish my wife's hairdryer would adhere to this rule!
I really don't know if using the burner on the inverter which is MSW will harm it but I guess we will find that out the hard way.Like I said before they are not expensive.The burner can be easily replaced.
Time will tell if the change is a good thing.For now it appears to be an improvement over the propane.
We love the cooktops and they have made food prep more enjoyable for Kris. She readily agreed that if we have no shore power or could not use the generator she would "bite the bullet" and go out to eat! LOL