Of course the 1000 watt heater would cost much less to operate for the same period of time, but it would not heat the same amount of water or raise it to the same temperature as the 4000 watt one would.
BINGO!
Watts = POWER.
ENERGY is not just power, it is power over TIME.
(Making up numbers here to illustrate point)
500 gallon spa (in that vacuum bottle) with 2 heater elements; 1000W 120V and 4000W 240V.
With 120V 1000W, it takes 4 hours to heat up the spa. Net ENERGY consumed is 4kWH
With a 4000W heater, it takes 1 hour to heat up the spa. Net ENERGY consumed is 4kWH!
4kWH = 4kWH, no matter how you get there. Current is irrelevant, demand is irrelevant, voltage is irrelevant, 1 phase or 3 phase is irrelevant.
That's how it works guys.
My earlier point was only that because (in this example for instance) the pump MUST run with the heater element, and the smaller heater element is going to take longer to heat up a given amount of water, then the pump will need to run longer and MAY mean more energy will be used FOR THE PUMP.
But Charlie B made a good point: the salesman made what ends up being an unqualified statement. We have no idea if he was comparing equally sized heating elements at 120V and 240V. We have no idea if the 120V unit compensates for a possible longer running time by providing a smaller pump, but therefore less "action" in the spa. We have no idea even if the compared spas held the same amount of water. So really, we cannot answer the question AS POSED. If however we ASSUME that all other things were equal, i.e. same amount of water, same size jet pump, but lower wattage heater on 120V because of circuit size restrictions, then I still contend that the 120V version would likely use
more net energy.