the advantage of a traditional LCD display with backlight is high refresh rate, low pixel response times and full colour, so you can watch video on it an scroll around dragging pictures without smear or blur. these require constant power to keep the image on screen. LED just means the image is lit with LED light, this is how pretty much all LCDs work these days. it used to be there were CFL and LED LCDS, early LCD displays were lit with high voltage fluorescent tubes before LEDs became cheap enough and bright enough to be the better option.
E-Ink on the other hand moves physical pigment particles around in an oil to form an image that works by reflecting ambient light, just like print on paper, no power is wasted on bright LEDs to make it viewable in a lit room or daylight, a small light is used for low light viewing. They are perfectly readable in direct sunlight and once the image is formed it requires zero power to maintain and can stay viewable almost indefinitely, so they are extremely power efficient when used properly. their disadvantage is they take a measureable amount of time to form the image so video or smooth scrolling are not possible and they are mostly greyscale.