Although short answers are preferable to long ones, the Xbox 360 resolution question in the FAQ is incomplete and not really correct.
- The 360 *does* support 1080p over component, though many TVs don't support that format. Happily, the 500m/600m does!
- The exception to this is for DVD/HD-DVD content -- when connected by component, the 360 will display DVDs at 480p and HD-DVDs at a maximum of 1080i.
- VGA does 1080p for all sources -- games, video content, etc. However, VGA forces you to use "PC mode," which doesn't include nearly as many picture adjustments, the colors and gamma are out of whack, and the black level is lighter. (I admit I haven't kept up with the various KRP threads so there may be a workaround for this by now)
Overall I think component is probably a better choice. You get the accurate color, gamma, etc of video mode AND 1080p resolution. You are limited to 480p with DVDs, but the 360 isn't a great DVD player in any case. HD-DVDs are probably a pretty niche concern at this point, and I'm not sure that the 1080i "limit" is a big deal anyway. For one thing, with 1080i you can use advanced mode to get real 24p via reverse 3:2 pulldown.