Light output (brightness)
Winner: LED LCD
Loser: Plasma
Runner-Up: CCFL LCD
Without question, LED LCDs are the brightest TVs you can buy. Some models are capable of well over 100 footlamberts. To put that in perspective, in a movie theater you're lucky if you get 5. CCFL LCDs are a close second.
Plasmas just aren't that bright. It's all relative, though, as plasmas are still likely way brighter than old-school CRT tube TVs. So plasmas aren't "dim," but they aren't nearly as bright as LCDs.
The question is, do you need that light output? In a dark room, 100 footlamberts will be searingly bright, and could cause eye fatigue. In a bright room (daytime/sunlight) a plasma might be hard to see.
Another aspect to consider is any antireflective or antiglare material on each screen. A plasma with a really good antireflective coating may be better to watch with room lighting than a glossy-screen LCD with no such coating (and vice versa).
Black level
Winner: Plasma
Loser: CCFL LCD
Runner-up: LED LCD
This is getting a lot closer, but plasmas still offer the best black levels. Yes, LED LCDs can sometimes have an absolute black (by turning off their LEDs), but when you're watching a movie, plasmas are going to seem darker. This relates to contrast ratio...
Contrast ratio
Winner: Plasma
Loser: CCFL LCD
Runner-up: LED LCD
Contrast ratio, or the ratio between the darkest part of the image and the brightest, is one of the most important factors in overall picture quality. A display with a high contrast ratio is going to seem more realistic, and have more virtual "depth." I highly recommend reading this article: Contrast ratio (or how every TV manufacturer lies to you).
There are a trio of exceptions. The Elite LED LCD (made by Sharp) has an advanced local dimming backlight, which gives it a plasma-like contrast ratio... for a price. A big price. Sony's HX950 series also has local dimming, but hasn't received as high praise as the Elite. LG's 55LM9600 even less so. One good LED LCD doesn't make them all good, nor does it herald a new generation of better LED LCDs. The Sharp/Elite doesn't do anything new. It's a local dimming LED LCD. We've actually seen fewer and fewer of this types of displays for the reason the Elite makes quite obvious: price. Local dimming LED LCDs are more expensive than edge-lit models (and much more expensive than plasmas, at the same size), and these days, expensive TVs aren't big sellers.
Do a few other local dimming models come close to the better plasmas (or exceed the lesser ones)? Yes, but again these are the exceptions, not the rule. Check out LED LCD backlights explained for more info.
There are some technologies coming down the pike that may offer even better contrast ratios. One of the most exciting is OLED. I'm really excited about OLED. It promises to be the best of all words: the best picture quality going, ultra-efficient, and incredibly thin. To learn more about this upcoming TV technology, check out What is OLED TV? and OLED: What we know.
So, on average, plasmas have a better contrast ratio (with notable exception noted). If you're curious why they don't look like it when you see them in a store, check out Why do plasma TVs look washed out in the store?
Viewing angle
Winner: Plasma
Loser: CCFL LCD/LED LCD
Runner-up: IPS LCD (see text)
How big is your room? Do you or loved ones sit off to the side, viewing the TV at an angle? If so, it's important to note that LCDs of both flavors lose picture quality when viewed "off axis," as in not directly in front of the screen.
Small room, small couch, mother-in-law Barcalounger off to the side? Don't worry about it.
Somewhere in the middle are in-plane switching LCDs, which offer a better viewing angle at the expense of overall contrast ratio and black level. Check out my article Myths, Marketing, and Misdirection for more info.
Energy consumption
Winner: LED LCD
Loser: Plasma
Runner-up: CCFL LCD
No question, LED LCDs have the lowest energy consumption, especially when you turn down the backlight. Prius drivers, this is the TV for you. CCFL LCDs are a close second, with the same addendum.
Plasmas, especially when you turn up the contrast control (which you need to for them to look their best), just aren't as energy efficient. They are, however, far better than they were a few years ago.