Good question by the way, I'm glad to educate. First, with 1080i and 1080p, the number designates the number of lines and the letter designates the way it's scanned, progressive or interlaced. Progressive scans the lines all at once, while interlaced scans half of the lines (one on, one off, one on...etc). Here's the kicker. 1080i scans half the lines every 60th of a second, producing a full picture every 30th of a second. 1080p scans all of the lines every 30th of a second, producing a full picture every 30th of a second. From that, it sounds like there isn't a big difference, but the actual difference is in the display panel. IF you have an HDTV capable of 1080p, great. Use the HDMI cable. If you don't have a 1080p HDTV, great. Use the HDMI cable. Which brings me to the second question. The xbox 360 is a digital source. With component cables, which are analog, you are downconverting the signal to analog, sending it over analog cables. You WILL lose a little bit of quality in this process. The HDMI cable however is a digital cable. Additionally it is a single cable. (If you have a surround sound system, you need to be using it. The 360 should have an optical out for surround, so use that.) Either way you look at it, you should use the HDMI cable no matter what. If you haven't made a TV purchase yet, consider the 1080p models. However, the 360 doesn't put out 1080p unless you bought the add-on HDDVD player. If you did, great. You will need a 1080p TV in that case. Sorry for the long read, hope it helps.
I have the Xbox 360 HDMI cable and a Xbox 360 : elite, I'm wondering what is the real difference between 1080i and 1080p also HDMI vs Component HD?