Isn't Orthodox Christianity split on this matter? With Eastern going one way and Oriental the other?
Yes and no. Virtually all of the Oriental Orthodox are Miaphysites, or better said Non-Chalcedonians. They believe that the divine and human natures of Christ are completely combined without any remaining distinction. Greek Orthodox, for example, believe that Christ has two natures, fully human and fully divine.
This has pretty much become a distinction without a difference, words of men trying to express the nature of God with each trying to do their best initially to fight Nestorianism. I can go to an Oriental Orthodox parish and receive the sacraments if an Orthodox parish isn't available and the same goes for the Oriental Orthodox. We have Armenians, Ethiopians and Egyptians in our parish who are technically Non-Chalcedonians and they are fully involved.