
It is a truism that converts tend to be more observant than those born into a faith. This is particularly true among the Orthodox. For example, my friends who are converts to Orthodoxy observe the fasts with great strictness, abstaining from meat, dairy and fish during the times of abstinence. On the other hand, the local paper lists several Orthodox churches in the area who have fish fries during Lent, and a couple that serve macaroni and cheese as a side dish. To generalize, ethnic Orthodox Christians have a more relaxed, if homey, attitude toward their faith, while the converts are more zealous, with all the good and bad that implies.
These contrasting attitudes have often led to conflict between the ethic Orthodox and the newcomers, and not too infrequently among the converts themselves, mostly former evangelicals. Indeed, every person I know who has converted to Orthodoxy has been traumatized by strife and division.
Byzantine Catholics have more or less escaped the trauma, though it is true that “converts”- most often Latin Catholics who have gone east, and therefore not technically converts- tend to embrace the Eastern way while ethnic Byzantine Catholics often mix east and west freely (the Melkites in general are the exception and have always been the least latinized of the Byzantine communions). This has not led to conflict because the situation is different among Byzantine Catholics. For one thing I have never heard of a Byzantine Catholic parish where former Latin Catholics are the majority, while there are whole parishes in Orthodoxy composed completely of converts from Protestantism (with a few former Catholics thrown in). Indeed, there is one communion- the Orthodox Church in America- where the majority of bishops are former Protestants (and yes, it is a mess). Thus, those of us who have traveled the road to the Catholic east tend to keep things quiet, to not disturb the waters. But conflict or no, the phenomenon exists.
But rather than leading to division, those in the Byzantine churches who desire a more faithful adherence to tradition work quietly to encourage a more pure praxis.
And that begins with education. My own parish has contributed immensely to informing both eastern and western Christians on the contrast and harmony of east and west with a recent presentation at the parish, ” About East and West”, by Archimandrite Damon Geiger,which has gained widespread interest on the internet; it can be viewed in its entirety here:
Reflecting on this, Ric Ballard of the Eastern Catholic Spiritual Renewal blog talks about the different spiritualities behind the rosary and the Jesus prayer, so externally similar with their beads and repetition:
http://easterncatholicspiritualrenewal.blogspot.com/2012/01/rosary-vs-jesus-prayer.html

My experience here is quite different. I haven’t seen the pacific Latin -> Byzantine vs contentious Evangelical -> Orthodox difference. I’ve seen the same number of problems in both locales. The numbers will differ, though, as many Latins with those problems eventually become Orthodox.
As a convert to Orthodoxy from Roman Catholicism, I have to say my experience is not yours. I have not been traumatized by strife and division by becoming Orthodox. I left most of that behind in the Latin church. I don’t experience the OCA to be a bigger mess than any other church group I’ve known. I used to practice in a Byzantine Catholic church. Lovely people, but neither fish nor fowl, and obviously second class Catholics as far as many Roman Catholics were concerned. All churches have their problems, and Orthodoxy is no exception, but I do not think your description is accurate across the board. In some cases, yes-in others no.
I write from my experience, which is limited to a handful of parishes in Ohio, and to a handful of Orthodox friends, as well as the very public squabbling in the various Orthodox jurisdictions. I’ll take both of your words for what you have seen, but it is hard for me to think that anything in the Byzantine Catholic communions rivals what I have known to have occurred in Orthodoxy. Among my friends I know of two (all convert) parishes which have been disbanded, one OCA and one ROCOR. One of my friends had been on the parish council and was sued by former parishoners. He was so traumatized that he hasn’t practiced any faith for over a decade. And I’m sorry; there is nothing to rival the sparring bishops of the OCA or the Antiochean Orthodox.
There has been strife in my parish, but it had to do with the personality and actions of the pastor, not anything theological. And when people have gone over to Orthodoxy they did so quietly, without rancor.
All anecdotal, I know, but that is what I have seen.