Many Eastern Catholics, in obedience to the Vatican’s mandate that we be fully what we are, i.e. “Orthodox Christians in Communion with Rome,” maintain a vision of the papacy that is somewhat more in line with what Holy Orthodoxy sees as being the papacy’s role. Christ is the head of the Church, not the pope. The pope is the “Patriarch of the West” (a title sadly not adopted by Pope Benedict XVI), and as such he has direct relevance only for Western (i.e. Roman, Mozarabic, Ambrosian, etc.) Catholics. The Eastern Catholic Churches all have their own heirarchical structure. For example, the primate of the Melkite Greek Catholic Church is Patriarch Gregorios III (Laham). He occupies the first chair within the Synod of Bishops for the Melkites. I don’t know that I would go so far as to say he is the “head” of the Melkite Church. He is more like the “older brother” among the other Melkite bishops, each of whom are the primates of their own eparchies (diocese) and are equally entrusted with preaching the Gospel and maintaining Holy Tradition in their own eparchy.
On the Universal level the Pope operates in much the same “older brother” fashion. He is there to guide and give advice when that guidance and advice is sought after, but he ought not to meddle in the affairs of other particular churches unless called upon by those churches to do so. Sadly this is not always lived out.
I hope this helps a little. The situation of Eastern Catholics is really somewhat of a gray area, maybe better understood as a battlefield. We are the Easterners who live out that future communion between Catholics and Orthodox that is being so ardently sought after right now. As such we are often misunderstood by our Western brethren because we “think like Orthodox, act like Orthodox, walk like Orthodox, talk like Orthodox, celebrate Liturgy like Orthodox,” etc. Many of us, taking seriously the words of Cardinal Ratzinger in a number of his writings and lectures, even reject Western dogmas that were declared after the East/West Schism. We don’t reject them as heresy; we simply reject them as being outside of our Patrimony, outside of our Tradition (a Tradition equally as ancient and venerable as that of the Latin West). As a result of this we are often seen as not “Catholic enough” for Roman Catholics. Conversely, however, since we recognize that there is something important about the “Petrine Ministry,” we are also often seen as not “Orthodox enough” for the Orthodox.
Be that as it may, we are what we are. Personally I believe that when unity is finally achieved both the Orthodox and Catholic parties will have much to be grateful for to those Eastern Catholics who were courageous and bold enough to fully live the Eastern Tradition, despite the opposition, misunderstanding, oppression, and persecution that they have suffered through over the centuries.
