Let's point these out, so that in future you can make a better educated guess at your choice of new HDTV screens.
Is a screen made up of two sheets of glass, with gas pockets making up the individual pixels. These gas pockets act like a fluorescent light tube, and radiate different colours when charged with various electrical signals.
Liquid Crystal Display. Two sheets of glass (or other transparent sheets, but we will assume glass for now) are filled with liquid crystal, and light is shone from behind the sheets of glass. Depending on the electronic charge, the liquid crystal either allows light through or not, thus forming an image. There is far more to the technology, but this is a very basic explanation.
The Pros and Cons
The life of the Plasma or LCD
In earlier versions of the Plasma screens, the life of the screens was between 15 000 and 30 000 hours. The LCD did have a longer life span, at around 50 000. Both Plasma and LCD these days should give you around 60 000 to 80 000 hours. At 6 hours viewing per day, it equates to at least 27 years. I doubt you need to worry about the screen, because by then we will probably be watching 3d holograms, if we're watching anything at all! With Plasma screens they talk of the "half life" of the screen, this means that the gas in the screen can only display half as bright or dark as before, basically giving you a very "dull" picture.
Plasma screens give off more heat than LCD screens.
On screens bigger than 50", Plasma will give you the better image and normally will be cheaper than the LCD.
LCD screens do not suffer from image burn, where the same image is displayed on the screen for a long time. When the screen is off, you will notice that the image is burnt into the screen. I am told that Plasma screens are not as bad as they used to be. In normal viewing, burn-in should not be an issue.
Energy and weight
The LCD uses less electricity, and weighs less than Plasma.
Plasma screens will give you better viewing with fast action shots. I would imagine if you enjoy fast moving sport on TV, Plasma would be the better choice. This is normally calculated by the refresh rate of the unit.
Plasma screens do not like being poked and prodded, however LCD screens can get scratched - of the two, the LCD is more robust.
Plasma screens are prone to reflections from the room in well lit areas, due to the technology used and the flat glass screen. Make sure the manufacturer has something like anti reflective coating, anti reflection or anti glare, as these are critical to stop the reflection on the screen. LCD screens have matt finishes on the screen that prevent this effect.
LCD will give you a brighter image.
The contrast ratio of a Plasma screen is normally higher than that of the LCD. The black on the Plasma is far darker than that of an LCD.
Plasma screens will have a greater viewing angle, which allows you to view the picture from either the left or the right of the screen and not directly in front of the screen.
LCD is freely available at 1080p resolution, however Plasma is only now starting to launch new products at 1080p.
Best for Plasma screens
Best for LCD screens.
So what does all of this mean? Check your room where you will be installing the new screen to asses the brightness of the room. Analyse what sort of TV viewing you do as a norm. If going for a Plasma screen, check the half life of the set. Check your room layout, and see if the viewing angle will play a part.
In the end, try and find a store that emulates similar lighting to your viewing room, then play a DVD of your favourite, or a well known movie and see what the image is like. Also they say that a Plasma image is closer to the image we see on our CRT (old TV sets), where LCD is more crisp - sometimes perceived as artificial.