Not sure they are that far apart. One of the issues that separate the two ancient churches is Petrine Primacy. Orthodox theologians have not rejected the concept of primacy, but only its development by the Church of Rome.
In November of 2004, Pope John Paul II manifested his desire for Christian unity when he handed over the relics of Saint John Chrysostom and Saint Gregory Nazianzen to the Orthodox Ecumentical Patriarch Bartholomew I in Saint Peters Basilica. In his message to the Patriarch, the first among equals of the Orthodox Churches, the Pope said that the return of the relics to the See of Constantinople is "a blessed opportunity to purify our wounded memories, to reinforce our path of reconciliation."
Now, continued the Popes messge, is the "propitious moment" to pray so that God "will hasten the hour in which we will be able to live together, in the celebration of the holy Eucharist, full communion, and thus contribute in a more effective manner to make the world believe that Jesus Christ is the Lord."
"I will never cease to seek firmly and determinedly this communion among the disciples of Christ, stated the Pope in his message, as my desire, in response to the will of the Lord, consists in being servant of communion 'in truth and in love.'"
Following Pope Emeritus Benedict XVI's decision to step down, Patriarch Kirill of Moscow sent Benedict a letter in which he says:
I have warm memories of our meeting when you were elected to the Roman See. During your ministry we received a positive impetus in the relations between our Churches, responding to the modern world as a witness to Christ crucified and risen. I sincerely hope what developed during your active participation, a good trusting relationship between the Orthodox and the Catholics, will continue to grow with your successor.
These dialogues have been ongoing, behind the scenes and without great fanfare. Let us pray that they continue under Pope Francis so that, as our Lord requested, we all may be one (John 17:22-23).
I have vast respect and affection for the Orthodox, and I wish to learn a great deal more; and love a great deal more.