Aye, Orthodox/Miaphysite have some nifty perks. As a liege, you have free excommunications on all people who share your religious head. If you avoid the pentarchy, this means everyone in your realm and independents in your de jure kingdom who arent kings, along with being immune to excommunications. This alone is ridiculously awesome, and much more useful than any Crusade or invasion on a larger target.
And if youre Orthodox, you can mend the schism... nothin like making everyone either a closer ally or holy war target. Sadly, the Pentarchy as Miaphysites or Orthodox/Miaphysites heretics doesnt seem to be much more than a fun goal. A goal Im close to: Nubia holds Alexandria, Jerusalem, and Antioch.