If you own an Apple product such as the latest iPad, iPhone 4S, or MacBook Pro (the latest version), then you have seen one of the boldest advancements in display technologiesRetina Display.
[Update: There are other phones with better than Retina Display now]
This is the Apple standard of displaying content with pixelation that human eye cannot detect. That means if you view your Apple screen from a natural viewing distance, you will not be able to distinguish any pixels. This makes Retina Display a ravishing new development as far as display technologies go.
On the other hand, Samsung has pioneered in developing new display technologies for handheld devices, and they have come up with Active-Matrix Organic Light Emitting Diode (AMOLED) technology (an improvement over the OLED system). ‘Super AMOLED’ and ‘Super AMOLED Plus’ are variants of this. You will find a comparison of Retina and AMOLED here.
Architecture of Mobile Displays
AMOLED as the name suggests is a display based on organic compounds, which luminesce on contact with electricity. The display has an organic layer above a thin film transistor (TFT) substrate that injects electricity into the organic layer, making it generate the necessary colors. Look at the image here.

The individual pixels on AMOLED are capable of creating their own light, and hence they don’t require a backlight unlike other liquid crystal displays. This is one of the reasons why AMOLED gives the best possible black levels.
Retina display by Apple employs the traditional LCD TFT with IPS (In-Plane Switching, made to widen the display angle, pioneered by Hitachi) technology, but they have made the pixels too tiny to notice (78 micrometers as claimed by Apple). Thus iPhone 4S is capable of displaying more pixels per square inch. iPhone 4S has a ppi ratio of 326, one of the highest among smartphones today. To get some advanced information about Retina display, go to Jonesblog.
Power Consumption
LCD displays require a dedicated backlight to generate colors. This is also the reason why LCD doesn’t give you perfect black levels (even to display black it needs backlight!). This obviously increases the power consumption level of LCD.
Winner: AMOLED
Clarity & Color Reproduction

Viewing the image on an LCD screen and an AMOLED screen and then judging the consistency of clarity would easily suggest the superiority of LCD over AMOLED.
The latter has a problem with sunlight. It doesn’t display well under it. In fact you wouldn’t be able to recognize if the phone is turned on or not under sunlight. This is the reason why Samsung innovated and developed a variant known as Super AMOLED that displays better under sunlight.
AMOLED has another issue. It gives an oversaturated image and doesn’t come up with the naturalness in colors. However, LCD screen generates the most natural of colors. Considering the pixel density and brightness of Retina display, Apple has scored here.
Winner: Retina Display
Pixelation
You will not notice any pixelation on iPhone or the latest iPad. High ppi ratio and small size of pixels make the display lifelike. On the other hand, you can notice a slight amount of pixelation on AMOLED phones like Samsung Galaxy S3. Although this is not exactly a display technology issue, we still rate it here.
Winner: Retina Display
Display Thickness
As you saw earlier, OLED displays lack one layer, the backlight. This makes the display much thinner than the Retina display.
Winner: AMOLED
Viewing Angle

OLED displays have no bar on their viewing angles. Retina display on the other hand employs IPS technology to improve their viewing angles.
Without this innovation, LCD screens have just the same viewing angle as old laptops. The clarity goes down as you move to a side.
With LCD IPS, Apple has achieved excellent viewing angle on iPhone. However, AMOLED display is like a printed paper when viewed from the sideit’s clear and blemish-free.
Winner: AMOLED
Brightness and Contrast
Apple iPhone 4S is brighter than Samsung Galaxy S3 at the first look. The Retina Display regulates brightness of the screen efficiently so that you get the best battery life and the best brightness. However, if you go higher on brightness or try to achieve the same amount of brightness on both the devices, you will find AMOLED screen on S3 to be slightly brighter. Check this image out from Engadget…

Winner: AMOLED (due to savings on battery life).
Conclusion
Looking at the display technologies available today, you can expect to see several developments in the coming years. Also, there are a lot of other technologies out thereOLET, SED, QD-LED, FLD, etc. Difference between AMOLED and Retina is that the former is one of the best new technologies and the other uses the best possible improvement on an existing technology.