This is a good question to display the difference between ‘efficient’ and ‘effective.’ Electric heaters are more ‘efficient”; they are 100% efficient in turning electricity into heated water. Both electric and gas heaters lose heat from the jacket as they sit there all day, but that is about 4% loss. Gas heaters are about 80% efficient in coverting gas into heat. So the electric heater is more ‘efficient.’
However, the gas heater is more ‘effective.’ It will cost about 1/3 an electric bill to run a natural gas water heater and about 1/2 the electric bill to run a propane gas heater. Also, the gas water heater will reheat the tank of water in half the time an electric heater takes. You get hot water for other uses faster. So gas heaters are about twice as ‘effective’ as electric.
Many folks have ‘efficiency-mania’ going for expensive highest-efficiency units over ‘effective’ units – not knowing the difference.