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This comparison is NOT a true reflection of energy use over time; only the costs to heat one tank of water from a cold start.
Heating tank from cold start would only be when tank is new or when service is interrupted


How much does it cost to run tankless water heater
Tankless fuel cost calculator Estimator

Estimates made are for new water heater in perfect operating environment.
Calculations do not consider longer-term effects of hard water, inefficienceies caused by high temperature
settings, fluctuating temperature of incoming water.
Natural Gas daily cost
Volume of   Temperature BTUs EF rating BTUs   Actual
Hot Water H2O Weight rise in required of the purchased Cost per daily cost to
Heated   degrees F to water heater to heat therm heat the 
      heat water   water   water **
64 8.33 77 41,050 0.62 66,210 $1.2000 $0.795
Electric
Volume of   Temperature BTUs EF rating BTUs   Actual
Hot Water H2O Weight rise in required of the purchased Cost per daily cost to
Heated   degrees F to water heater to heat KW/hour heat the 
      heat water   water   water **
64 8.33 77 41,050 0.94 43,670 $0.0841 $1.076
Propane Gas
Volume of   Temperature BTUs EF rating BTUs Cost per Actual
Hot Water H2O Weight rise in required of the purchased gallon daily cost to
Heated   degrees F to water heater to heat propane heat the 
      heat water   water   water **
64 8.33 77 41,050 0.62 66,210 $1.2100 $0.875
Tankless
Volume of   Temperature BTUs EF rating BTUs Cost per Actual
Hot Water H2O Weight rise in required of the purchased gallon daily cost to
Heated   degrees F to water heater to heat propane heat the 
      heat water   water   water **
64 8.33 77 41,050 0.82 50,061 $1.2000 $0.656

How to clean-sediment-out-of-water-heater

How much does it cost to run water heater


Gas and electric water heaters

Resources:
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How to install electric water heater
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