Which type of monitor (LCD or CRT) is of higher quality?
This depends on what you mean by "quality." If you are talking simply about the quality of the images that can be viewed on the monitor, then I would say that a cathode ray tube has higher quality than a liquid crystal display.
As you can see from the link that I have attached, CRT monitors are able to show much better images than LCDs. They are, for example, able to show colors in a way that is much more faithful to reality. This is a major aspect of quality.
If you have a broader definition of quality, however, LCDs may be more competitive. If quality includes portability and weight and such, then LCDs have a huge advantage. They are also less likely to flicker.
So there are many benefits and drawbacks to each -- follow the link for much more detail.