It depends. HDMI supports resolutions up to 1080p and can allow digital video sources to remain in the digital domain all the way to the display (which in many cases today is itself a digital device, such that the video signal never has to be converetd to the analog domain). As a result, HDMI can offer a better picture than component for certain cases. Additionally, upscaling DVD players are not allowed to provide an upscaled video output over any connection except HDMI, so for players that offer superior upscaling to that built into your HDTV you can only benefit from that upscaling via HDMI (component caps out at 480p).