I've got a Pentium 3 machine with a WinFast A340 (GeForce FX 5200) and it has an S-video, VGA and composite (yellow) video output. My TV has composite input and component (red, green, blue) input. The video card had an S-video to component adapter cable. I know there is certainly a difference between composite and component on LCD HDTVs, but on a tube TV, is there a significant difference in clarity between the two types of inputs?
Tube TVs are typically SD (Standard Definition) which is 480i (640x480 interlaced).
There will be little or no difference between composite vs s-video because of the low quality resolution and inherent blurring effect of tube TVs. You could try buying higher quality cables (gold plated) but I wouldn't guarantee that you'd see a huge difference.
SD tube TVs just aren't very good when attached to a computer unless you're doing strictly video playback. Because you need a certain level of sharpness to read the fine details of a computer display (fonts, controls, etc).
Compared to HD, which starts at 720i (720x1280 interlaced) SD just looks cheap. Plus, the image on a flat panel plasma/lcd/oled TV is so much sharper because they don't suffer from the 'memory' effect of the phosphor used in SD TVs. HD need a much higher refresh rate (60hz+) to cut down on motion blur but they look much sharper. Think of the phosphor in a tube TV as being the same stuff in glow-in-the-dark stars (because it basically is). It slowly fades out until it is recharged by the RGB beams that draw the screen.
For more info on the differences between types of cables see this link.
While the difference between standard definition and high definition is pronounced, even on a tube TV (assuming that it supports HD as it supports component input), with your configuration, you will not be able to output at a resolution higher than 480p (640x480).
S-video is limited to 480p, and an adapter for it will simply upscale the image to 720p/1080p which may or may not increase the quality of the image, but, especially on a tube TV, could cause the image to appear slightly sharper and blockier. Your desktop would still be stuck at 640x480, however.
The difference then, in your case, is effectively 480i vs 480p. 480p will have a slightly crisper look, but on a tube TV, the difference will not be as pronounced as the difference between 480i and 1080p.