Jim: The U.S. Department of Energy indicates an induction cooker is 84% efficient at energy transfer, versus 74% for a smooth-top electric unit.  My tests of kitchen-range gas burners find that a 10,000 BTU/hour gas burner transfers about 3,500 BTU/hour into the water in a standard pot and 5,000/hour into a HX pot.  10,000 BTU/hour (= 3kW) is a very common rating on home gas stoves and on many of our camping / backpacking stoves that use white gas, butane, or propane.
There are 3,412 BTUs in a kilowatt-hour, so your 1800W induction burner would transfer 1800/1000*3412*0.84 = 5,200 BTU/hour (and be quick to start and stop heating like gas is). Definitely superior in heating rate, heating efficiency, and quick response to traditional open-coil or flat-top electric-resistance elements. Â And better than gas with a standard pot. Â Very similar to gas with a HX pot.
The 3.3kW induction cooktop would be even faster heating (as would commercial gas burners at 20,000-30,000 BTU/hour and even more so with HX pots).
My gas is $0.94 per ccf (100,000 BTUs) while my electricity is $0.23/kWh (3412 BTUs). Â So to boil 100 gallons of water from 70F would cost:
$3.17 using gas and a standard pot
$2.22 using gas and an HX pot
$9.46 using electric induction
$10.74 using electric resistance
But YMVV: most of the country has cheaper electricity (especially the Pacific NW) and most of the country should have cheaper gas – Henry Hub is at $0.27/ccf while our local wholesale price is about $0.70.
Your cooktop doesn’t add up to much usage, but your water heater does.