A complex question. If we limit our discussion to just these poems, we can see some differences. Coleridge treats Xanadu as more explicitly imaginary, forcing the Orient more directly into the realm of the fantasy, and the fantastic. You can see this from the use of Xanadu on, with details like "incense-bearing trees" suggesting that the entire landscape of the Orient is in some way managed, a kind of stage setting for desire. (Of course, the "pleasure-dome" suggests this as well.) It is as if the Orient is a great Harem for Coleridge.
By contrast, Byron's Orient, while still Orientalized, is more grounded in historical reality. Individualized names and concrete details abound, and the emotional texture is more conflicted and complex. It is still Romanticized, but it is more like Byron is reworking the existing East, rather than imagining it.