I don't know if the Xbox 360 does 1080p output, but if it does, you'll be golden with this. To get 1080p output, you MUST use HDMI, so it may be an upgrade they'll do.
You *need* HDMI to get 1080p (the best possible right now), but component will do for 720p. Can't tell you much more about the Xbox 360.
Obviously not... The 360 outputs 1080p via ALL it's HD sources including component, VGA and HDMI. Therefore your statement is fallacious.
Grizzly man, dependent on the quality of the monitor and assuming it supports 1920x1080 via VGA, there is very little difference between VGA or HDMI.
I was actually experimenting today by chance on my 1080p monitor with a couple of games (Ninja Gaiden 2, and Virtua Tennis) both are 1080p native I believe.
Running at 1080p, 720p via HDMI - to 1280x768 & 1920x1080 via VGA I was hard pushed to spot the difference in any of them regardless of input or resolution.
The issue you will have to address with HDMI output on the 360 of course is that if your attaching it to a monitor rather than a TV, you have to work out the audio output.
If you don't buy an elite, and you get a premium with HDMI instead - it does not come with the optical output adapter.
However getting hold of one of those adapters over here is a fricking nightmare and can cost you €50 which is nerly the difference in cost between an elite and a premium. The 360's AV cable which has the optical output or the red/white audio jacks does not sit inside the 360 with the HDMI connected as there is not enough room.
But there is a solution, which means in order to get sound to an external source your going to have to do a bit of messing with the component/composite cable that comes with the 360 premium hdmi. You can simply remove the bottom piece of plastic from the cable and it will then allow enough room for both the HDMI cable and AV cable to be plugged into the 360 at the same time.