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.
And there are also autonomous Churches both in EO (Russian Church Abroad, Sinai, Japan, Finland, Estonia, Ukraine, China? Belarus?) and in OO (Armenian Churches, British Orthodox Church, Syriac Church in India, French Orthodox Church under Copts?). Each of these Churches belongs to a particular autocephalus Church e.g Japan to Moscow Patriarchate