We have a tankless water heater, generally used with the popup camper. We use a 20lb propane tank with it.
300 gallon hot tub, 2400lb water. To bring water from 50F to 100F will take 120k BTU.
The propane tank holds about 350k BTU, and the heater operates at maybe 80% efficiency. 150k BTU (80% efficiency for what we need to bring the water to temperature) is a little less than half the propane tank, so maybe $10.
150k BTU is equivalent to 43.5 kW*hr (1 BTU = .00029 kW hr). Marginal electricity is $0.29 at our level, placing the cost of a fill at $12.60.
Cost difference is minimal, but by using the tankless water heater, but 1.6 gal/ min = 100 gal/ hr = fill at temperature in 3 hours?