>>802887
It's almost a purely administrative thing inside the Church, you can belong to any church and it doesn't make a real difference since you're in the EOC (Eastern Orthodox Church) in either one of them, they have varying reputations from time to time but at the end of the day they're all in communion with each other.
This list may be incomplete but it explains the inside organization pretty well,
You have Rome where everything is much more Centralized in, well, Rome itself no questions asked, while the Eastern Orthodox Church takes a more decentralized approach somewhat akin to the Pentarchy, there is no fundamental difference as I said, they all subscribe to the same beliefs nominally and they're all in full communion with one another at the end of the day all being part of the Eastern Orthodox Church as a whole, and this deeper inside organization is almost purely administrative and you shouldn't bother with it much.
Some have different reputations (Russian, Georgian and Romanian ones being more true to the faith and unmoving while something like GOARCH has a notorious reputation for straying away and taking things more liberally) but it's mostly superficial and you shouldn't bother with it much again because it ultimately all depends on every individual parish.
This decentralized administrative structure makes things more flexible in many ways and if one center piece is to fall (like Constantinople for example) it's ultimately, not a damning catastrophy that results in a complete breakdown but rather it leaves room for other Patriarchates to take over.