There are two kinds of LED screen, ones which are really an LCD but use LEDs for backlighting and ones which use OLED to produce the light.
LED back lit LCDs tend to be more energy efficient and because the brightness of the LEDs can be changed very quickly, they sometimes use dynamic brightness control to increase the perceived contrast. LEDs are also low voltage devices and physically smaller that conventional CCFL backlights so the screen can be thinner and a high voltage inverter is not required.
LCDs work by blocking the transmission of the backlight to make the screen dark so full power is always drawn into the backlight whenever any part of the screen is white, even if it is only one pixel.
OLED screens work by producing light rather than blocking it so a dark picture consumes almost no power and an all white picture consumes about the same as an LCD. An 'average' picture content requires far less current in an OLED display than would be used in an LCD so they are generally more efficient.
Brian.