The most important thing to remember is, you are happy with it. It was YOUR money that bought it. You are the only one that has to be impressed with it.
That said, congrats on the new TV.
What you are seeing with 1080, is the pannel scaling the 1080 signal to the pannels native 1366X768 resolution.
With DVD on the Xbox, CSS prevents resolutions over 480P over component. I don't realy know what the upscaling capability of the Xbox is. I would try both and see which ones you like best. Do you have an AVR with HDMI switching? Then you can run both of them HDMI
Anywho...have LOTS of fun with your new TV.
j