The difference between the two is Component is analog and HDMI is digital. HDMI also carries digital audio. Component does not.
HDMI also has HDCP whereas Component does not.
Most of the movie companies limit the output to 1080i over component, because of the lack of HDCP. The only device I have ever seen output 1080p over component was the XB360 and even then, only if you had a HD DVD accessory drive hooked up...
My Apple TV doesn't give me the option of choosing 1080p with out having an HDMI plugged in..
I was going to reply yesterday that the max. supported resolution on component was 1080i, but i didn't have an Apple TV to verify. My new Apple TV was waiting when I got home and the HDMI cables I ordered weren't, so I scrounged the component cables from my Xbox and like BigAudio do not see any option for 1080p over component.