The EOC is divided into 14 autocephalous Churches (15 if you count the OCA, but the EP doesn't recognise it as autocephalous). Each is ruled by either a Patriarch, Archbishop or Metropolitan.
The OO Church is divided into 6 autocephalous Churches: the Copts, Ethiopians, Eritreans, Syriacs, the Malankara and the Armenians. They are ruled by Patriarchs and sometimes a (or more than one in the case of the Armenians) Catholicos. The OO Churches each have a great deal of autonomy and independence and there is no boss on earth of the OO, unlike the RC. The OO do have a Pope in Alexandria but he's only the Patriarch of the Copts. He isn't seen as infallible and doesn't have universal jurisdiction or all those things the Latin Pope has.