EO & OO are two of the closest Christian groups in terms of theology and practice.
We aren't in communion because of the disagreement over Christ's natures.
We, as Eastern Orthodox, say that Christ has two natures, a human nature and divine nature which are united in one hypostasis, or one in substinence.
They, as Oriental Orthodox, say that Christ has one nature, which is both human and divine.
This, arguably, is the only real separation between us, the other differences could probably be worked out once we are in communion with each other.
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Whereas, the difference between Eastern Orthodox and Roman Catholics, or Oriental Orthodox and Roman Catholics are numerous and the degree at which we are separated has greatly worsened over the last 1,000 years with the many innovations that the Roman Catholics have made to their faith. Originally our dispute began over the authority of the Pope, who was trying to extend his authority over the whole Church (which was an authority he never had) and a dispute over the addition of the word "filioque" to the Creed.
However, since that time, the Roman Catholics have added so much to their faith that never existed in the Church, such as the idea of Purgatory, the Immaculate Conception of Mary, the Assumption of Mary (as opposed to her Dormition), Papal Infallibility, Papal Supremacy and Universal Jurisdiction, Original Sin (as opposed to the Orthodox idea) and many other innovations.
So for us, and from our perspective, the Eastern Orthodox Church and Oriental Orthodox Church are both the most pure representations of the Original Church. Obviously also, as Eastern Orthodox, we know that our Church is the Church founded by Christ and his Apostles. We would also say that the Oriental Orthodox are extremely close to us in faith, probably closer than any other two Christian communions out there.