For HD-DVD players, you can access high definition content and resolution through either the HDMI or Component Video connections. However, you can only access high definition via both HDMI or Component Video on Blu-ray Disc players manufactured before January 1st 2011. After that date, access to high definition resolution via component video connections is at the movie studios' discretion, and, as mentioned above, component video connections will be eliminated entirely from Blu-ray Disc players after 2013.
The reason for this is that although the Component Video connections allow owners of older, pre-HDMI, or DVI-HDTV-equipped, HDTVs to enjoy the benefits of Blu-ray and HD-DVD, video signals traveling through component connections are more easily pirated that than those the travel through the digitally copy-protected signal traveling through an HDMI connection. Since HD-DVD is now discontinued that is no longer an issue for that format, but the movie studios and related content providers have successfully required Blu-ray disc player manufacturers to reduce any potential video piracy issues on Blu-ray Disc players sold in North American market.
However, also at play is the general transition from analog to digital video, and with fewer analog TVs and HDTVs that do not have HDMI connections in use, the need for either or both composite and component video connection options on a Blu-ray disc player is less and less. It is interesting to note these connection changes are not being aggressively pursued for cable/satellite boxes, network media players/streamers, or game consoles. However, as time goes on, you will see fewer analog connections on those devices as well.
To sum it up - If you want to access high definition video from a source device, whether Blu-ray Disc player, HD-DVD player, or other source device, you best best is using HDMI. You really need an HDTV to see the benefits of either Blu-ray or HD-DVD.