Console plug formats?

I have a Nintendo Gamecube and a TV that supports high definition output. I’d love to get the component cables that enable my Gamecube to look so spiffy, but I can’t help feeling I’m getting ripped off: the adapters for the PS2 and XBox are each $7.00, whereas the adapter I think I need to buy is $35.00! Is there any chance that two of these three proprietary consoles have used some common interface for video-out, so that I could use one of the cheaper cables with my Gamecube?

Or do I have to suck it up and pay five times as much for a minor improvement in picture quality?

Bonus Question: Dopers who have their Gamecubes running to component output, how much is the picture improved over the S-Video version?

Unfortunately, they are all probably proprietary. For what it’s worth, I have connected my Xbox to my TV using all possible connectors at one time or the other and the difference in quality in S-video vs. component wasn’t nearly as much as standard composite vs. S-video. If it were me, I’d be OK just using S-video, but that’s just me and of course, I’m using Xbox - Gamecube might be different.