This issue has alot to be said. CRT and LCD screen both have good and bad things about them. First off lets point out a few definitions here, there are CRT screens which are much like TVs, then there are their cousins the Flat screens which are still CRTs but are based on Sony's Trinitron Technology, giving you a totally flat screen - hence the name. Then there are the Flat Panels, now flat panels are often referred to as LCD screens, but this is not always the case since Plasma screens also fit into this category and yet are based on an entirely different technology.
Ok, now the good and the bad:
CRTs display brilliant colors, mutiple resolutions based on the users preference, they support a full viewing range(This simply means that you can look at the screen from any angle and still see the same perfect image) and of course they are cheaper than Flat Panels. On the downside though CRTs are large and bulky, have tremendous weight for their size, generate ALOT of heat, and consume a great deal of energy!
Now if you remember Flat Panels come in two flavors but generally share the following attributes - incredibly small and compact, extremely light weight, comsume far less energy than CRTs, and generate very little heat. On the downside - usually more costly and can be viewed well in only one resolution!
For LCD screens you also need to add the fact that it has a very limited viewing angle, usually only up to 30 degrees in any direction from center, deveate from this viewing area and you get dark and light areas. Then there is glare, LCDs do not take sunlight very well, too much and you won't see much on the screen.
Plasma screens are for the most part perfect in that they possess the best that CRT and LCD screens have to offer - they can be viewed at any angle and display colors as brilliantly as CRTs. They are as small and compact as LCDs and produce little heat and use less energy. There downside usually includes cost which is usually more expensive than LCD which is already higher than CRTs and on top of that there are very few manufacturers that have been making Plasma screens for computers.
Now I am not sure how you use your computer but hopefully all this may help you