There is a lot of different LCD screens, and the newest LED backlit models have "full backlight" that use a large number of LED's and this gives one big advantage to the image quality: dynamic contrast ratio.
Getting charged an arm and a leg for that priviledge, twice the going rate for plasma.
A color TV is most challenged by making black. And how well a screen can do black has a big affect on the color, and contrast ratio is an under appreciated quality of TV's.
Neither plasma not CRT are black challenged.
Another important quality is the speed of the pixels to turn on and off, and at first this was a challenge for LED's, but they are now are quick enough to show high speed motion.
Some people are reporting getting headaches from LED TVs, it is possibile to turn on and off too fast.
I am trying to keep track of TV's in the 40-42" size for the day my current TV stops working. As time goes on, the better 1080P 120/240Hz TV's are tempting - my Panasonic GAOO 27" Superflat has 500 lines of resolution which is great for its time, but it uses ~165watts. I'm definitely getting an LCD with LED backlight, because 35-50watts is far better power use, and the picture quality is much better than what I have.
Some of the strange artifacts that LCDs (or the circuitry that supposedly makes improvements) leaves a lot to be desired.
That said plasma has its own issues. The front is always glass because there's x amount of pressure behind it. If there's even the slightest unnoticed crack on the interior of the glass it can eventually spider out, the way auto windshields tend to crack more in the winter. Such "defects" are always blamed on the user and are not covered under warranty.
LED - Some of the "240 Hz" rates are merely pulsing the LEDs to make it seem like higher refresh rates. In layman's terms that's called a marketing gimmick. There's are also widespread reports of banding, to the point where the unit becomes unwatchable.
I have an NEC LED pc monitor. It has light leakage just like the prior model with a CCFL. Actually it's slightly worse and its brightness uniformity is not better either. The only positives appear to be power consumption and the lack of mercury. But even then to be truly "power efficient" one needs to factor in both the energy used in manufacturing and the disposal costs of the unit. Anything less than that you're simply fooling yourself. These days 1 and 2 year old TVs, washing machines, refrigerators, microwaves are filling up dumps and we truly don't understand (or even admit) what the long term costs of this mess will be. I digress.
I gotta laugh at people who say plasmas appear dull in bright rooms. Ever go to a bright movie theater? Actually it's a reasonable tradeoff, slight dullness in bright light versus wonderfully correct color at night. I hand calibrated my set with minimal background light, I couldn't care less if its dull on bright sunny days. Why would I watch TV at such times? More incentive to turn it off and be outside, a positive thing.