As far as I know, component is not capable of handling 1080P.

Whether you use HDMI vs component depends somewhat on equipment. For instance on cable/TV boxes, you are usually better off using component as cable boxes (including the Motorola that Verizon uses for its Fios TV fiber over TV service) are horrible at properly handshaking with TVs over HDMI.

On the other hand when using an upconverting DVD player, Blu-Ray or HD-DVD player, you should use HDMI. The Oppo players for instance pass much higher quality video over HDMI vs component (for the older models that still have component out).