Based on what I read about dogs in Orthodox churches (as derived from Russian sources), there is some suspicion of dogs especially as they’re seen as dirty. I don’t know if this attitude does exist outside of the Eastern Orthodox churches, whether if it does exist among Oriental Orthodox churches at all.
Both of them do have their differences, most notably the idea that Jesus’s human and divine natures are one and the same. When it comes to places like Armenia and Ethiopia, it could be influenced by the localities they’re in to an extent. However among certain Ethiopian biblical based texts, there is some distrust of dogs.
But it could also be metaphorical at that, though if they’re closer to the original Christianity (which shared a lot in common with historical Judaism’s distrust of dogs) there could be some degree. If Oriental Orthodox churches are counted as part of the Eastern Orthodox church, especially early on there could be but who knows.