Pre-warning: this technical breakdown of Component vs. VGA for the XBOX 360 - to determine the best cable to use for your high-definition TV. 

Conclusion: for all intents and purposes, VGA and Component are too similar for it to make a difference. Each has its strengths and weaknesses, but they're very similar. They're both analog, so they both suffer from imperfect reproduction too, so it comes down to the preference of the user.  Read on for the technical differences.

Note: This comparison was written after the Spring 2007 Update for the XBOX 360 Dashboard.

Component uses a Y Pb Pr color scheme, and uses sync on all cables IIRC. This lets them cut costs because the Pb and Pr outputs can use cheaper DACs or cables, since they include the color information where resolution isn't as important (not everyone does this). On HD resolutions, the sync is tri-level, which doesn't affect the video signal, as it doesn't shift the DC offset.

VGA uses an RGB color scheme, and separate sync. This means you need more connector pins, but you remove the issue of the sync. VGA connectors are not ideal for video signals, but in general it isn't an issue (RCAs used in Component are better). Sync-on-green VGA carries regular sync on the Green cable (this is the system used in RGB video through SCART connectors). This requires the monitor to know about the sync and be able to set the proper reference level, which is why if you simply separate the sync out using an LM1881 and feed it to a monitor, it will often show up with green blacks. With a monitor that supports SoG natively, this isn't an issue, as it's designed to handle this properly.  As for the Spring 2007 Update for the XBOX 360, it probably does what others have written: shift the color range and black level to proper VGA values, getting rid of the washed out effect of the XBOX 360.

Both can carry HD resolutions. Both essentially carry RGB video (most systems render to RGB color and then convert to YPbPr for component). Component requires the sender and receiver to do a colorspace conversion, VGA doesn't (this might have a small impact in quality).

This probably doesn’t help, though it is going to come down to two things; (1) Your viewing source and (2) your personal preference.  Both sources can carry 1080p (analog), but to carry the 1080p signal via component, your TV must have the ability to do such. The XBOX 360 is going to do what it is going to do, and the end result is going to be most effected by the consumer in their television purchase and personal configurations.