The LCD monitor does have several significant advantages, mainly: Naturally flat screen (no curvature), much smaller footprint, less moving parts to wear out, and no problems with focus or blurriness (each pixel is independently owned and operated; no electron gun to go out of whack). The CRT still has the advantage in cost (though LCDs are gaining as the technology matures), response time (LCD pixels generally take at least 20milliseconds to change states, which limits your effective frame rate on movies and games to 50FPS or less), and overall picture quality--as in, you don't get burned-out pixels on a CRT. With an LCD, you may have to accept as many as a dozen dead pixels before the manufacturer will agree that it is defective.
My philosophy on buying a monitor is, get the best monitor you can afford. Skimp on the CPU or RAM if you have to, an extra second or three won't kill you, but a bad monitor will contribute to decaying eyesight.