I believe the US version of this is the Optoma EP706...
http://www.projectorcentral.com/Optoma-EP706.htm
There's no straightforward answer other than to point out that this is a SVGA projector. It isn't 1080i, but is 800x600 which means that if you are filling the screen, that's what you get. If you feed it 1080i, the projector must scale that signal down to 800x600 to fit on the screen, so you are losing a great deal of information, but with video, this typically can be done fairly cleanly.
Anything about SVGA, such as XGA, or up to the max accepted resolution of 1400x1050 will be scaled down to fit inside the SVGA area. This is going to throw out a certain amount of data and always leads to a softer image.
Now why does it look so bad? I'm not exactly sure really. If you are using a VGA connection from the PC to the projector (not component) it may pass through a different scaler than the X360 passes through using component. If you aren't using VGA then you may be feeding it an oddball resolution, or the wrong signal type, or even a lower resolution such as 480i.
Since computers have different video cards that behave differently, it could be any number of things actually related to the computer, and not the projector, but you may want to try a different PC if you can.