Component vs. HDMI ... at the same resolution things shouldn't be any different, apart from the cabling itself.
There is huge advantage using HDMI if the both end of devices are capable of handling digital signals. All the modern displays such as LCD, Plasma, or DLP are digital. All the modern video players such as DVD and BluRay are also digital medium. With HDMI there is no unnecessary digital to analog conversion, and the original signal will be preserved without any degradation. The component video is analog. If you use component video between DVD player and LCD display, then DVD player will convert the digital video into analog using its video DAC, and LCD display will have to digitize the analog signal for display. No one should be using component video except in the case of high end CRT projectors.