The divvying up of North America is a trouble not only for Catholics but also for Orthodox. Of course for the Orthodox the issue isn’t much about different traditions, rites, and even theology. Most people believe it is the Patriarch of Constantinople holding on to her largest diocese. Given her traditional territory is all but Muslim land now. Other Orthodox are fighting for an American Orthodox Church, Russia has already granted autocephally to the OCA which the EP has yet to recognize.
For the Eastern Orthodox, there are 5 recensions in use in the US, not counting the two syncretic rites… Ruthenian (ACROD and UOC), Pre-nikonian Russian (Old Believers), Nikonian (OCA, ROCOR), Greek (Greek orthodox), and Syro-Byzantine (Antiochian Orthodox).
They do have differences in theology, in the exact same way tha the Ruthenian Catholics, UGCC, Russian GCC, and Melkites have (fairly trivial) theological differences leading to somewhat less trivial differences in praxis. And note, also: the Russian GCC has parishes using the OCA-Nikonian, ROC-Nikonian and Old Believer texts… the latter two only in Russia… but all three expressions approved by Rome.
Constantinople’s Patriarch is trapped by law - both Church Law of the Contantinopolitan Patriarchate, and of the Turkish civil state. It is, sadly, fading to near insiginificance, being eclipsed by the Monks of Mt. Athos, and by its cadet Patriarchate, Moscow.
Ecclesiology is fundamentally different in the Greek Orthodox Church from the rest of the Byzantines - and is an expression in praxis of major divergence in praxis of a tiny division in theology - the metropolitan-archbishop as vicar of christ, rather than the diocesan bishop.
Russian Ecclesiology likewise is subtly different from the others - stronger patriarchal authority.