Scholars agree today that Rome held a certain primacy, and the Pope did so and so, but both the actual boundaries and the origins of his position were not given a strict definition. So there were different perspectives, both East and West, at different times and places, interpreting the Papacy differently depending on circumstances and what was convenient. Stupidly enough, no councils were held to really affirm or deny what the Pope can actually do and why he can do it. The Pope's primacy was simply accepted.
Then the Gregorian Reform came around and finally cemented a view to be held for good in the West. The East remained more or less ignorant of the exact Western doctrine and its implications until the fourth Crusades, the sack of Constantinople, the Pope's response to it, and the Latin occupation.
The Orthodox never really strictly defined the Pope's job and boundaries actually, except by saying that the Catholics are wrong. Indeed, the only issue that was dogmatically addressed since the schism is the filioque.
Because the issue simply didn't have a single answer until nearly 1000 years into the Church's history, both Catholic and Orthodox apologetics are hard to take seriously since they just disregard the historicity and development of the other side. So do your own research on what you think makes the most sense, I guess.
t. orthodox