Yesterday, Microsoft's Major Nelson announced a new update for the 360 fixes issues with 1080p over VGA. If you want 1080p, then you have two choices currently: component or VGA. My TV (a 46" Sony XBR3 LCD) will only accept 1080p over VGA or HDMI.
Well the fix is here, so I ran to Best Buy today to get a VGA cable (I was using component).
And guess what? It works! I have full 1080p now!
To tell the difference between 1080i and 1080p, you need content that is running at 60 frames-per-second. I don't currently have any, so my visual quality hasn't improved...yet.
I recently found out that I could generate my own HD content on a PC and burn it to a DVD and the 360 will play it back. When I get some good test videos, I'll post my results.