Define vastly.
Show your math to support your claim.
Not that you care, but the word 'vast' appeared in the English lexicon around the late 1500s', coming from the French word 'vaste'. It means 'large number' or 'great extent'.
It's really too bad you never learned English.
Here is the reason electric water heaters are more expensive:
Heating a given quantity of water always requires the same number of joules.
Natural gas (methane) has a certain number of joules per mole available by burning it. That doesn't change. There is, however, no waste heat. ALL of the heat goes into the water you are heating.
Electrical power is generated at a power plant. Waste heat occurs in the generating equipment and in the method used to turn the generator shaft. From there, the power is converted to high voltage for transmission. That transformers generates waste heat. The current on the high tension lines also generate waste heat (if overloaded, such as the lines feeding the SDTC (formerly California), the wires will actually sag from just this waste heat (possibly touching a tree or something). At the substations, that voltage is traded for higher current again for distribution lines to homes and businesses. More waste heat. More current on distribution lines also generating waste heat. At the home or business, ANOTHER transformer converts distribution voltage down to that used in the home or business. More waste heat occurs there. Even the fuse attached to said system generates waste heat.
By the time electricity reaches the electric water heater, you have spent almost as many joules in waste heat as what is going to heat the water. In other words, electric water heaters use almost TWICE as many joules to heat the same quantity of water as natural gas would.
This problem is even worse when comparing EVs to ICE vehicles. Charging an EV also generates waste heat in the battery and in the charging circuit. Note the car isn't even moving during the charging cycle. As the EV is driven, MORE waste heat comes from the battery (again!) and from the motor(s). This is why batteries AND the motors are liquid cooled. To create heat, more effectively cooling the battery and motor. EVs also use almost TWICE as many joules as a gasoline car would to move the same size vehicle the same distance. Note that F=mA still applies, and the electric car is much heavier than the gasoline car.
That's the math, dude.