In response to the latter part of this thread, the differences between the EO Churches and the Catholic Church often amount to be the EOs misrepresenting our doctrine (e.g. saying we mean two spirations by inserting the Filioque when we do not). Other things tend to be new objections created by neo-palamite bias against anything that appears to have a tinge of Augustine/Latin/Scholasticism (e.g. objections to original sin, indulgences, the numbering of the sacraments, etc. which were never a point of contention until the mid to late 19th century). Studying the EO synods post-schism, but prior to the neo-palamite movement shows an acceptance of most that is now supposedly rejected.
It’s also difficult to pin down one common doctrine among the EO Churches on various issues. Livenotonevil’s posts are good example of this. Some of the things he is promoting (like no grace outside the EO Churches) are by no means an agreed upon truth among them.
That being said, Catholics can also be guilty of misrepresenting our relationship to the EOs. While they can be said to have a relationship to the Church based on a common baptism and other sacraments, they cannot be said to be “part of the Church.” The one Church professed in the Creed can only be said to be the Catholic Church (branch theory is not a valid perspective under Catholic doctrine). In other words, the Church of Christ can only be said to subsist in the Catholic Church, not anywhere else.