A Facebook friend of mine is an acquaintance from my days on the orthodoxchristianity.net forums, and is now an EO priest. He had made a joke about turning a church over which he has some kind of influence (maybe it's in his parish or something [if indeed "parish" is the right word for EOC], I'm not sure) into an Emergent church, and then said "...or not, LOL" or something to that effect. I commented that there seem to me to be numerous similarities I've noticed over the years between EOC and the Emergent church. He asked me to PM him a rundown of them, and I paste my response here:
Just a few ways off the top of my head.
For one thing, EC (ie, Emergent Church, as opposed to EOC) patterns itself after more mystical theologians, with prayers such as hesychastic prayers, centering oneself, controlling one's breathing, seeking the contemplative part of worship, etc. Use of icons, incense, candles.
EC puts a strong emphasis on community and the voices of the community, which is very similar to the way EOC recognises post facto out of all little-t tradition the big-S Sacred big-A Apostolic big-T Tradition that it acknowledges as authoritative and normative for the church.
Following that, EC has a strong errantist streak wherein the Bible is not held to be without error. It ends up being subservient to traditions from within the church (or "the community" as ECs like to say). Same as in EOC, and quite different from evangelicals or Reformed.
In many EC congregations/communities, the Eucharist is a big central deal. (I actually wish that my own SBC church would make the Eucharist a bigger more central deal and am about to teach to that effect in my Sunday School class; I've asked the elders to do so but not really seen much change.) In EOC, of course, the Eucharist is also fairly central to worship.
There's a strong streak of political liberalism and Social Gospel-type orientation toward action in both EC and EOC.
Similarly, since EC is basically (theological) liberalism 2.0, 'salvation' is not viewed as getting right with a God Whose Law has been gravely transgressed and trampled on by sinful men, but rather it's growing this world towards a fair and just society in which God is honored thru everyone living out the love of Jesus in everything all the time. This is far more similar to theosis than to a Reformed/evangelical understanding of justification+transformation/regeneration -> sanctification -> glorification.
Hope that helps!