Plasma is "better" in a dark room technically. You get wider viewing angles from plasma and deep contrast ratios. The negatives are that plasmas aren't as bright as LCDs so in a well-lit room the plasma won't appear very bright and might also reflect light off the screen. They also use slightly more power than LCDs but not a huge difference. Plasmas are more fragile and should be professionally installed (unless you're an expert). In a darker room you can't beat a plasma, but bulb life and burn-in are also conerns over the long haul.
I prefer LCD's because they look great during the daytime if you have your curtains/blinds open. They are more durable... you pop them out of the box and set them up easily yourself so no need for professional installation. They use less power. There is basically no glare from other lights in the room or from sunlight. Their contrast ratios are getting better and better and now the top tier models rival the deep contrast ratios of good plasmas. LCDs also have a long bulb life (you should get at least 5-7 years of watching great picture quality before you begin to notice even the slightest dimming of the picture). The negatives are that LCDs have a sweet spot where the picture looks as good as possible, and outside of that angle/distance the picture won't be quite as good. If you're sitting at a very sharp angle (like a couple feet from being parallel to the side of the TV) it will be hard to see details in the picture. This is kind of an overblown quality though... the only time it really comes into play is if you have a huge party with a ton of people trying to watch a game or a fight on one LCD or if you have like 4 peeps playing a video game and another few people watching the action from side angles. Also, in my experience LCDs are practically immune to burn-in. One last negative I remembered... if you're trying to sleep in a room with all the lights turned off and just your LCD on, it's almost too much to bear. The TV is so bright that's it's almost overwhelming in pitch blackness.
All in all, I just love LCDs a lot more, but there is nothing wrong with plasmas. I'm also not a big fan of DLPs... their bulbs burn out a lot quicker than LCD or plasma.
If I were recommending an HDTV for a first time buyer I'd say go LCD and you'll be more than satisfied.
Sharp, Samsung, Sony, LG... can't really go wrong.
Of the mid-tier brands, Vizio has good bang for the buck.
Hope this helps