Well, the EO author is not alone in this understanding of, “If, therefore, the Greeks or others say that they are not committed to Peter and to his successors, they necessarily say that they are not of the sheep of Christ, “ Note, some translations say “when the Greeks,” which is how the Catholic Encyclopedia has it. (http://www.newadvent.org/cathen/15126a.htm), and which states this “Bull is universal in character,”and affirms that “for salvation it is necessary that every human creature be subject to the authority of the Roman pontiff.” However, as with so many other authoritative pronouncements, this is held as open to some interpretation and can be and now is held by Rome in a way that “subject to the authority” is not as strict as it sounds, while the sedevacantist schism contends otherwise. (http://www.romancatholicism.org/eastern-schism.htm)
“she is as one denomination seeking to have dominion over the faith of all.”
You don’t seem to have a grasp of ecclesiology. The Catholic Church is not a denomination like the Baptists or Lutherans or Presbyterians.
You left out the context and the qualifying word “effectively she is as one..,” for as said, “Rome can claim universal jurisdiction and the power of coercive punishment,” but in this respect she has no real power over any but her own, having lost her unScriptural use of the sword of men (apart from the Swiss guards)
The difference between Protestantism and Orthodoxy is that the former is a heretical movement and the latter is in schism.
That depends upon who is defining “heretical.” The New Testament church was birthed as a “heretical” entity according to those who sat in the seat of Moses, as they saw church failed of the requirements of authenticity in doctrine and formal decent of office. Yet the authenticity of the church was established by conformity to the what was written and the manner of supernatural attestation it affirms God giving to new revelation, abundantly referencing the then-established Scriptures, which body it would complete, and the Lord working with them, with signs following. (Mk. 16:20) And by such is the church of the living God manifested today, in correspondence to its claims, primarily via the preaching of the gospel of grace effecting manifest regeneration, to the glory of God. Amen.
The Orthodox have retained the priesthood and the sacraments.
However, though i know you know Greek, from what i know the New Testament church did not ordain a separate class of sacerdotal priests, it was not priests that were formally ordained but bishops/elders, as the Greek word “presbuteros” is not the formal word for “priest” in the New Testament, nor does it denote a unique sacrificial function distinctive from the “laity,” as it simply means “senior” including as denoting a senior position, while episkopeō (translated as “bishop”) means “superintendent” or “overseer.” [from “epi” and “skopos” (“watch”) in the sense of “episkopeō,” to oversee, (Strong's)] See a little more here.
I’m a Greek Catholic and not a Greek Orthodox because papal primacy and jurisdiction,
I see.
But conciliarism is just as errant as Ultramontanism, which John Paul II condemned as heretical.
We feel much the same. But some Catholics want to “canonize” JP2, while others lambast him, including for being too conciliatory.
I’d stop reading polemics written by Ultramontanes who think every papal utterance is infallible if I were you because it does not reflect the contemporary magisterium.
I did not think most on that side go that far, but perhaps see everything in an encyclical as infallible (i suppose these are neo-ultramontanes), while others deny that all that Trent said was infallible teaching, or even that Vatican Two was. And But ultramontanes like Manning were doctors of the church who are invoked as needed by Roman Catholic apologists as representing Roman doctrine, and so we must choose between which variant of Roman Catholicism that is contended for.