It isn't just an issue between CRT and LCD but between any two display devices. Even two CRT monitors of the same type can display radically different colors. Also it isn't just chroma which is off but brightness contrast and often gamma too. You will also notice a significant gamma difference between Mac and Windows systems.

When a creative studio needs to make sure that everyone sees the same thing on their respective monitors, they use a monitor calibration device to set every display to the same predefined profile. One that is cheap, easy to use and geared towards the consumer is the Gretag Macbeth Eye One calibrator. Be aware that if you have a cheap CRT monitor it will be difficult to calibrate and wont hold its calibration for a very long time. Always keep a CRT monitor switched on once calibrated and recalibrate every 2 weeks. LCD holds its calibration setting permanently but the screen itself might fade slowly over time.

Once LCD and CRT monitors are matched you will still notice a slight difference. LCD will display deeper blacks due to its inherrently greater contrast.