Here' a quick mental dump for what it is worth...
No matter what the size and type of display panel type you consider - the video and image processing play a HUGE part in the quality of the image. Each panel technology has it's strengths and trade-offs. It's like asking if a pear is better than an apple. Both may be fruits but there are two very different things.
Plasma
These have the best colour gamut of all the panels. Colour reproduction is real life and skin tones look natural. Examining skins tones between panels is usually a good litmus test of a TV.
The largest players were Pioneer with their Kuro range and Panasonic with Viera.
Plasmas produce near perfect blacks - without any artificial circuit wizardry. This is because each pixel is an individual gas chamber which can be individually controlled for luminance and colour - without any lag.
Manufacturing costs are inhibitive with this technology - not least the cost of Phosphor. Both Pioneer and Panasonic found it increasingly difficult to justify the price premium in comparison to LCD counterparts which to the vast majority of people were adequate.
I have to stress this is not old technology. Pioneer decided to bail out of producing plasmas due to a change in consumer demand and the cost of sustaining their fabrication plants.
Panasonic - make there own panels and image processing circuitry. I cannot stress how important this is...the Viera processing engine is recognised to be one of the best.
The myth about the panels fading...is a bit of a fake argument. Most plasma panels can display way above the comfortable viewing range of brightness. This brightness is not the fake rating given for LCD panels where they artificially exaggerate certain aspects of the image to give the impression of brightness. Anyway, to cut a long story short...plasmas have built in circuitry to hold back brightness over the lifespan of the TV. So, even if you have the contrast and brightness set to 100% the TV records the time the panel has been used and compensates for it - by as much as 30%. Well over a period of 5 years of the life of the TV before you start experiencing the fade effect.
Plasmas to do not suffer from viewing angle issues. The image will look exactly the same from any angle - vertically or horizontally. LED and LCDs have an optimal viewing angle before the image starts looking a funny shade or hue of the true image.
LED
Best ones around that I have seen so far are from the Samsung and Philips range. Samsung are also one of the three largest manufacturers of display panels across LED and LCDs.
These panels can suffer from colour saturation problems, i.e. basic colours such as red, green, and blue can jump out and look unnatural. Sanyo have taken a different approach to the traditional RGB pixels - but with limited success.
Can suffer from video lag between video source and display. Don't understand how or why...but its a common theme across these. May be its the way LEDs behave....
On the positive side LEDs panels are very slim as each pixel can control its own light and so no back light is required. This is probably the future. Despite the panels being more expensive than LCDs the fabrication cost is actually less as there are fewer panels which fail the quality checks which has plagued LCD production.
Viewing angles are an issue if you do not watch your TV dead on. LED panels have better viewing angle range than most LCDs.
LCD
Can suffer from video lag when changing colour of pixels. This is where you get smearing and ghosting of moving objects.
Some manufacturers have tried to eliminate this by increasing the refresh rate of the image, e.g. 100Hz, 200Hz, 600Hz, etc.
These also suffer from bleeding back light and being able to maintain consistent brightness across the screen, as these typically use a lamp or 'backlight'.
Also there are two/three different types of LCD panels, TN, IPS and the other one I forget. But basically the IPS is the best one, i.e. is for colour and image response times.
Best panels I have come across are the Phillips range. The PixelHD video processing is one of the best ones around.
This technology is probably the most mature of the lot, but panels do suffer from the dreaded dead pixel syndrome. This is where a speck (or more) appear in the panel. The tricky thing here is that all manufacturers have different policies on how many pixels have to fail before they will replace the panel. Trust me, even when you get a single dead pixel on a 19" monitor - it drives you crazy.
Viewing angles are an issue if you do not watch your TV dead on.