This concept makes much more sense in my mind than I'm capable of putting in text, but I'm hoping the gist of the idea gets through.
It's been my experience that, in order to get the optimum "crispness" of graphical and audio capability, the television and system should be chronologically, and therefore, technologically equivalent to the style of connection (RF/coaxial, composite, component, HDMI, etc.) being used to join the two.
The big technological hurdle is matching the hardware at both ends of the connection. For instance, if you're planning on playing CC on a PS1 with the old composite AV patch cord, you will probably want to use a CRT, "box"-style TV, as those tended to be built around the use of composite connections as a primary source of input. In this scenario, the use of an HDTV would be technical overkill; it's an instance of the TV actually doing its job so well that the resulting image quality tends to be somewhat poor, as it would also display the impurities of the composite connection that aren't ordinarily seen on an older CRT screen.
Using older connection tech on newer TVs is like watching a worn-out VHS tape. It will work, but it might have you subconsciously rubbing your eyes in an attempt to get the image to come into better focus.
If you're actively trying to go HD, CC would probably look best if it was played on a PS3, using an HDMI connection. If the aliasing, or jagged-stairs effect, of the older graphics is a bit too pronounced, try using a PS2, a component (Y, Pb/Cb, Pr/Cr) connection, or both.
