To really appreciate the clarity of the LCD digital input if the way to go. This is what I hear, but I have never compared the two.
Regardless, the picture will be clearer than a tube, assuming you get a new one.
Almost all, if not all, of the standard tube monitors out there 17, 19, 21in, etc, are analog so you probably have analog monitor along with a video card with an analog output.
So if you go with a monitor with a digital input (has analog too, btw), you need to get a new video card that has the dig output.
So check on prices on that too.