What specific hardware are we talking about here? Are you hooking up to a satellite box or cable box and which one?
I can not see how an HDMI cable would cause slow channel changes. Actually, I'll go further and say that is impossible and here is my reasoning.
With a cable box or satellite box, the tuner which is changing the channels is in that box. The AV Input Output circuitry has absolutely nothing to do with that circuitry. Having a cable there or having no cable at all does not change even one tiny thing with respect to the tuning of the box.
Sound, is a little different issue. At some point in both your TV and whatever box you are connecting to, the HDMI circuitry and the audio circuitry for your component cables are different and follow a different path. Whenever that happens, it is always possible that because of a design error or because some electronic part in those circuits has drifted which would cause the different audio gains for the different paths. I've not seen it on my equipment, but it certainly is possible.
However, as an added comment, again, I do not know the TV signal source because you have not told us, but virtually all of it is currently 1080i at most and a good component cable should be able to handle that signal as well as HDMI. I also try to use HDMI but it is just because it is neater, easier, and sends control signals around to control things too. Not because it gives a better picture.