I'm Catholic but I have a great respect for and interest in Eastern Orthodoxy. I almost became Orthodox when I was converting out of protestantism but I became Catholic for reasons of convenience. Treat this question as one from a sincere seeker.
I had a few questions which protestants simply could not answer. For example
"Two or more protestants claim to have the Holy Spirit. They all go and interpret a given passage of scripture. They all come up with different and conflicting conclusions. How do you go about determining which one of them has the correct interpretation, if any of them do?"
Every protestant I've ever posed that question to has completely fumbled in response. They seem to misunderstand or not even recognise the fundamental problem which I'm posing. They fail to put themselves into the thought experiment and so fail to realise that THEY are the protestant with the conflicting interpretation. Some of them will espouse some nonsense about how "whoever agrees with scripture the most is correct", which is just begging the question. Some of them will be totally tribalistic and just assume that their interpretation is correct and anyone who disagrees is wrong: They don't seem to recognise that they are "playing pope", and so never get around to asking that crucial question "What gives me the authority?"
In any case protestants invariably end up completely failing to provide a compelling response to this question, which drives me away from protestantism and towards apostolic Christianity, which DOES have an answer to the question: ie, look to the dogmatic, holy tradition of the church; a church which can be identified by the apostolic succession of bishops. Anything which has been defined within this tradition is indisputable truth. Anything that it doesn't talk about is open to further interpretation and speculation until the church magisterium dogmatically rules otherwise.
The problem now is that there are multiple competing strands of apostolic tradition. How can I tell which one is the 100% correct, "Holy" tradition? And it is to this question that I have not yet heard a compelling response from anyone save the Catholic church.
I'll put it in a thought experiment again: Imagine that there is only one united church. However some theological dispute arises and splits the bishops down the middle: half of them are for the proposition in question and half of them are against. Each half anathematises the other half. How do you determine which half represents the true tradition and the true church?
From what I've gathered reading Orthodox blogs online, the Orthodox response is similar to the protestant response in the previous thought experiment. Orthodox will say "look at the church fathers, look at history, look at the bible. See how what we do matches up with that stuff more closely than anyone else. We must be correct!" But the thing is, the Catholics say exactly the same thing, as do the Oriental Orthodox, and the Church of the East. All of whom have valid apostolic succession and sacraments. How can you differentiate between these claims? Something else is needed.
In Catholicism this is where the crucial role of the Pope comes in. The Pope is that objective focal point for the entire church and the entire tradition. In the thought experiment just described, the Catholic solution is to side with the half of the bishops that are in communion with the Pope, and the other half are excluded from the church. This solves the problem neatly: The Pope is the visible centre to the church, whoever is connected to him is connected to the true church.
What foolproof method do you have for working out who is correct in the event of schism? To bring it even closer to home, imagine for the sake of argument that Eastern Orthodox are correct about Catholics and all the rest being entirely apostate. The Eastern Orthodox Church is the One True Church. But what if then the Eastern Orthodox church is split down the middle over some theological controversy? How do you determine which side of the schism is correct? Both sides are going to be yelling "Heretics!" at each other and both sides are going to be claiming to be correct. What Objectively foolproof way do you have for determining who is right? (similar to the Catholic method of "communion with the Pope"). Remember: Up to this schism both sides were getting along just fine and recognising each other as Eastern Orthodox Christians. All of a sudden all of that changes and lines are drawn in the sand, so how do you work out who is legitimate?