I don't know how Component vs HDMI effects digital TV, but here's what it does when we talk console games (running at 720p or upscaled 1080p):
Component cables transfer an analog signal, meaning there is a little bit of distortion, making the image appear smooth and soft, thus hiding image flaws, like one member pointed out.
HDMI is 100% digital, the cleanest signal you could possible expect from an HDTV. This means that whatever imperfections, flaws or anomalies the source may have, will be clearly visible. However, HDMI does offer more crispiness, sharpness and clarity. In some cases, even better colors. You may need to buy a good-quality HDMI cable (Monster comes highly recommended, but pricey), and tweak your TV for HDMI. You will definitely experience better sound with HDMI cables too.
In addition, HDMI may also offer slightly better motion clarity and screen refresh. Hope this helps.