Component and composite are two very different things. The main difference between component and HDMI is that the former is an analog signal, and thus susceptible to cable quality issues, interference, etc., but in the absence of those factors the picture quality between HDMI and component is basically the same.
In a perfect world, HDMI and component have the same image quality. The limiting factor these days are TV internals. Analog signal is an after thought for many manufacturers these days, so with many newer TVs HDMI is the only way to get acceptable image quality. You're correct, component and HDMI standards are capable of the same quality, but it all depends on the analog processor in your TV and how well the TVs upscaler handles analog signals.
Edited by ProppaT, 19 November 2012 - 03:15 PM.