Folks, my first degree was in electrical engineering. So I feel a little qualified to stick my nose in the 120 vs 240 debate.
Truth is, both sides of what have been said are right, but only if you like picking fly shit out of pepper for fun.
Theoretically, 240V is more efficient but has nothing to do with the light. It's the resistance of the wire between the box and the outlet.
240V has less losses due to wiring resistance. 2X voltage, 1/2 amps = 1/4 resistance.
But at the distances we will see this inside our houses, I doubt it would even be measurable.
Once the power is at the LED, as Grampa said the wattage is identical. It's an Ohm's law thing. The LED couldn't care less how you got that wattage there and will use it identically, producing identical waste heat for the amount of photons supplied.
Not trying to stir things up. Hopefully someone finds this useful.