Despite the myth that it does not do so, LED Displays consume lesser power consumption than other mediums of the same kind. The low power and energy-efficient part is the LED itself.
Even in TVs, using LEDs for backlighting saves 20% to 30% of power consumption. This consumes less power than cold cathode fluorescent lamps (CCFL) used in LCD televisions.
Power consumption actually depends on resolution, brightness and usage. For example, displays having different applications: indoor and outdoor. Both may have different resolution and brightness levels resulting to different power consumptions.