CRT's have useually far smaller refresh rates than LCDs. But this isn't the most imporant thing, the important thing is the response time, which is very high on LCDs (not so high anymore with state of the art ones, but still higher). And LCDs also have a far bigger lag/ghosting.
Colour management depends on make and model, and neither LCDs or CRTs is 'best' at this. Same with image shapes.
Also something very important is the contrast ratio, which is in general much higher on CRTs. LCDs are softer and more than often the black is actually grey because of the way LCDs work.
LCDs have far more chances of dead pixels than CRTs. In fact, with LCDs it is normal to have dead pixels and this is also calculated into the quality control before they are sold. Although now some brands have a "zero defective pixel" guarentee, but certainly not all.
LCDs can have more problems in displaying stuff in other resolutions than their own standard resolution and may produce slightly distored images, colors or artifacts.
LCDs have a far less viewing angle (though this can be a benefit, depends on your POV - also literally
-)
Older models put more strain on the eyes because of flickering (you may not notice it, but it does).
The only benefit LCDs have over CRTs is the low power consumption and low heat production and the small space they require.
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