Assuming you're talking about top-shelf CRTs and LCDs, the CRT will have much richer color and a brighter picture, while the image will be slightly less accurate than the DVI LCD. The LCD will be much easier on the eyes, but will show very slight ghosting. I don't know of any DVI CRTs yet, but
this whitepaper can show you some of the advantages of it. Personally I don't think it's a big deal for CRTs. You still have to convert the signal to analog once you reach the monitor. You're just gambling that the DAC of the monitor is better than the DAC of the video card plus any interferance along the monitor cord.