Don't know about power requirements, but plasma screens can "burn" images into them if the same image is left on the screen very long. They also have shorter lives than LCD screens. The advantage of plasma is that they can be made bigger much cheaper than an LCD screen, and their color reproduction is a bit more vivid.
The advantage of LCD is that they are sharper, last longer, and don't burn in images. The disadvantage is that their color reproduction is not quite as vivid as a plasma screen, but the difference is not that great. And a large LCD screen costs much more to make (and therefore buy) than a plasma screen.
All the broadcast video engineers I know recommend an LCD over a plasma unless you want a huge screen but don't want to pay a ton of money. The color difference is not that great, and the LCD's other advantages more than make up for this.