Technically, the files on the CD aren't AIFF format -- that's just the way that the Macintosh chooses to display them (and, as such, when you drag-and-drop an audio CD track off of an Audio CD, it is converted to AIFF on-the-fly). Back in the days of OS 6 and 7, when you inserted an audio CD, the files would show up as audio tracks of 0-length, and you could not copy them off the CD (they weren't converted to AIFF on-the-fly).
If you have Toast laying around, you might want to try creating an audio CD and trying that in the XBox -- my audio CDs play fine in my XBox, whether burned with Toast or iTunes. This may narrow it down to the way that iTunes is actually burning the CD if Toast happens to work...
I hope that helps, and I'm glad you found at least one way to make the CDs work!