One key point which I forgot to mention: don’t become Orthodox because you are frustrated with the disorganized and unclear state of contemporary Roman Catholicism, particularly the irreverent way the Novus Ordo Mass is often celebrated. You’ll find your fair share of political chaos in Orthodoxy as well, and while it isn’t as stark, there are liturgical abuses too.
To those above who claim that Orthodoxy is not sufficiently united, I think this is a bit naive. First, the sorts of problems and semi-schisms that happen in the Orthodox communion also happened in the ancient church. Various conflicts between local churches who severed communion with one another (but not with the other churches with which they both were in communion) were not uncommon- see, for example, the Meletian schism. Second, the problem of overlapping jurisdictions in American Orthodoxy (i.e. having both a Greek and Russian bishop in the same territory) exists in Roman Catholicism as well. Eastern Catholics have their own episcopal hierarchy which covers the same territory as the Latin hierarchy. There are three men who hold the position of “patriarch of Antioch.” The difference for Roman Catholics is that Roman Catholic canon law has normalized this situation, while Orthodox (while being quite lazy in seeking to resolve it) continue to affirm that this is an abnormal and uncanonical state of affairs.
If one speaks of doctrinal unity, it seems to me that Rome doesn’t have a leg up on Orthodoxy here, either. After all, most Catholics in the United States think that birth control is legitimate. There are many, many Catholic theologians and biblical scholars who teach very heterodox positions on Catholic doctrine- consider as an example Hebrew Bible scholar Mark Smith, who, while claiming to be Catholic, believes that Yahweh was originally a minor storm god on the early Israelite pantheon! Such cannot be reconciled with historical Catholic teaching, but he continues, with no official action. I bring these up not to rag on Rome and claim that there aren’t Orthodox scholars who do the same thing (there are) but to state that the situation vis-a-vis doctrinal unity is basically the same. Just because you can claim that the pope states the official position doesn’t mean you have unity. It just means that there is technically an official position, if a Catholic affirms Catholic teaching on the papacy.
Ultimately, these sorts of claims from both sides are an illegitimate attempt at a shortcut. The only way to sort through these issues is prayer and hard historical and theological legwork.
I think it’s a bit condescending to assume that the only reason one might become Orthodox has to do with one’s love for the Byzantine liturgy. This is a stereotype, but it’s not as common as you might think. I love both the Byzantine liturgy and the traditional Latin Mass. I’m Orthodox because of theology and doctrine, not smells and bells.