AMOLED is among the newest of the display technologies but uses an old system.
Direct LED display has been around a long time and is a very simple system. Basically each pixel is made up of three active devices which are directly lit to produce the output. In the past this produced a display that was lower PPI and lower brightness than that available for LCD but this is changing rapidly due to the newer AMOLED display. This system uses just a few layers shown in the figure at the left and is thus often more flexible and less expensive to produce than LCD. It also generally consumes less power. Comparison to LCD can be a bit more difficult with regard to brightness.
The brightness in an LCD is produced by a backlight which, in the latest iteration, is often done using pure white LEDs. The color is achieve by using active filters to create the color pixels that the user sees. Brightness is generally measured by simply turning on all of the color dots to create a white screen. Power consumption is determined by how bright you light the LEDs and is independent from the color. AMOLED display lights the LEDs directly to produce both the color and the brightness which are now linked. Thus power is now color dependent. Black needs no power at all while white takes the most power. However, this means that red, for example, only lights 1/3 of the LEDs so it may seem darker. To counter this the manufacturer will increase the power to the red LEDs to make the brightness "seem" independent from the color. This makes brightness very difficult to quantify since some brands measure brightness based on white while others use an average color value to specify the brightness (and power consumption). The design also dictates how well brightness is tracked through the color changes. The backlight is likely the biggest power hog in an LCD display device but there is more control and tradeoffs available in AMOLED displays.