I personally prefer Plasma, as Plasma is faster at refreshing the display compared to LCD. Maybe Plasma displays do not have a high contrast ratio's compared to LCD, or are maybe not so bright. They of course use more energy compared to LCD display. But i just prefer the way the picture looks on a Plasma display.
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I also agree what CDan says. There are good and bad displays. Having said i prefer Plasma. I would rather have a good LCD display panel rather than a bad Plasma panel.

Many manufacturers selling FULL HD TV's here in the UK are selling them from size 37 inch and above. I can't comment if that is the size at which point you notice a difference, or at the moment, it requires that size of display to accommodate 1,920x1,080 pixel resolution.