They do have some fundamental characteristic differences:
CRT (traditional monitor) - better contrast, better motion (no ghosting), runs at multiple resolutions, better color graduation (more colors)
Flat panel - brighter (emits more light), often less contrast, fewer colors (sometimes you see banding across smooth gradients), slower motion response (you see ghosting during a lot of motion), looks GREAT at it's native resolution, but will look a little chunky at any resolution other than the one it is manufactured at. Flat panels also take less power and produce less heat. I seem to recal some tech site doing a test with an ammeter (amp meter?) and showing that a CRT was consuming 60 watts while a flat screen was consuming like 13 watts.
Basically I prefer CRT for graphic arts and motion video work, but I prefer flat panels when I'm at work looking at text, spreadsheets, graphs, etc. I find flat panels very easy on the eyes but they're not accurate enough in terms of color, contrast, and motion to keep me happy when image or video editing (hobbies of mine.) Really expensive ones are good for graphic arts though.
I think Tomshardware.com recently had a comparison of 13 flat panel displays, you might want to look for it, as I remember it talked about some of the good and bad things about the newer, less expensive ones.