Power is the amount of work done per unit of time. It will have units of Watts which is equal to Joules per second. We determine the energy of each system above by multiplying the power with time. We do as follows:
E(heater) =1000 W (1 hr) (3600s/hr) = 3,600,000 J
E(bulb) = 100 W (24 hr) (3600s/hr) = 8,640,000 J
Therefore, the answer would be false. It is the bulb that consumes more energy.