With this question you have opened quite the bag of worms. This is generally suited for a large lengthy discussion, but I'll try to summarize. If you do but an LCD check the pixels response time, this is very important to it's overall performance. I believe an excellent rule of thumb is over 50 inches get Plasma, below that I'd stick to LCD.
Plasma pros:
- Better picture quality than LCD, generally, it excels at similar colors, especially black, which LCD's have trouble with.
- Cost effective for LARGE screens.
Plasma cons:
- Burn in of screen images that are kept up for a long time.
LCD pros:
- Cheaper.
- Better resolution, in terms of number of pixels.
LCD cons:
- The color black is difficult to display because of the backlight.
- Good luck finding a LARGE one, LCD TVs are a giant array of TFT's (a type of transistor) and it must be manufactured in one piece which is very difficult to do on a large TV.