There are 2 OO priests, 2 OO laymen, and 1 OO Bishop in my class at seminary. Aside from not accepting Chalcedon and the subsequent condemnations of some of their saints (Especially Severus), we have been hard pressed to find any significant theological difference. From what I can tell, the hard-line Monophysitism that existed around the time of the Schism no longer exists in their church. It speaks to the similarity of our theology that they can attend our seminaries to be ordained in their churches.
Even among the OO churches at the time of the schism, there was considerable effort to promote unity that would have likely worked if not for the hardline Monophysite monastics starting riots over the idea.