[photon]

As with all things like this the answer is it depends. Component is more limited in bandwidth so it really will only do 720p / 1080i. If you have a 720p TV then there will be very little difference between the two (as long as your cables are decent).

But if you are running new HDDVD or Bluray stuff, then with component you can definately be sacrificing some quality. The newer HDMI 1.3a specs allow for 1080p/24 which is 24 frames per second movies (the frame rate that movies are actually shot in). It also allows for more colours, so if you have a display that supports it you can get more colours.

Another aspect of it is copy protection. HDMI supports HDCP which allows encrypted materials like HDDVD and Bluray to play on the TV. Right now players will also send high def signals over component, but the option is there for them to turn that off in the future, meaning to get high def content your only choice would be HDMI (or DVI I guess, HDMI is just DVI with a different connector and audio).

One other consideration is the audio. I think most high def players require HDMI to be able to output their highest quality audio. If you are using the speakers in the TV it's not a big deal, but if you have a home theatre it might be. Without HDMI and an HDMI receiver, you'd be limited to Dolby Digital and DTS, where with HDMI and an HDMI receiver you can get the high def lossless audio.

Clear as mud eh? If you post the specifics of your setup we can probably give a more specific answer.