I wasn’t going to comment, I really was going to let this one go. But then I read the answers posted, and I couldn’t stop.

So, just to set ourselves up, we are talking about 1000 years of history here, from the arrival of Christianity in Rome in the mid to late 1st century (I would say at least by the 50s), and the Great Schism in 1054. The thing we must first realise is that Western Christianity (and by ‘West’ I mean basically draw a north-south line on your map roughly where Tirana, Albania is) diverged from its Eastern (and I will primarily talk about Eastern Orthodoxy, not about the non-Chalcedonian Church of the East and Oriental Orthodox churches) counterpart long before that Great Schism occurred, in fact, was probably moving in different directions almost from the start.

The first factor is simply language. The western half of the Empire was dominated by Latin, and the East by Koine (and later Byzantine) Greek. Although the church in Rome, and possibly in Gaul as well, originally functioned in Greek, they later switched to Latin (the liturgy switched around the 4th century; first Latin theological writings appear around ca 180; the most important western theologians apart from Irenaeus begin to write in Latin: Tertullian, Novatian, Cyprian, and so a Latin theological tradition develops).

Now, while Rome maintains links to the East, most of the churches west of Rome, and to some extent North Africa, maintain their primary connections with Rome. So ‘western’ churches are operating almost entirely in a Latin sphere. You see one evidence of this in the fact that all the so-called Ecumenical councils (Nicaea, Constantinople, Ephesus, Chalcedon, etc..) occur in the East, and have very, very poor attendance by Western, Latin bishops. They deal with theological disputes that occur primarily in Greek.

This linguistic divide is tied up with cultural divisions that develop over time, and also with liturgical development that runs along different trajectories.

Secondly, you have to deal with political matters. Once the empire was not merely nominally but effectively divided in two, they begin to operate relatively autonomously. This doesn’t go so well in the West, as we should mostly know by now, and the successive migrations of Goths, Vandals, Lombards, etc., and especially the Franks, causes significant change in the political, social, and cultural landscape of Western Europe. Especially when Illyricum (the modern Balkans) come to be dominated by the Huns, inter aliis, it severs the land-connection between East and West, further dividing their relations.

Connected to this, in the early to mid Middle ages, the rise of the Franks as the only real major consolidated power in Europe, and the only kingdom that is following Catholic Christianity (as opposed to the non-Nicene versions prevalent among Goths and Vandals), also has an influence on the general cultural and political milieu of Western Catholicism.

In all this time the East is not static. It is sometimes apologetically cute to say the Orthodox church has an unbroken tradition back to the earliest church (kind of true), but it changed and developed. in the East you have long and protracted theological debates over the natures of Christ (monophysitism on the one hand, dyohypostastism on the other), the development of a distinct Monastic culture, several periods of Byzantine intellectual flourishing, and of course the development of icon theology and practice in the midst of iconoclastic debates, which touch upon Western Catholicism but not in the same way.

Thirdly, of course, the Western Church has the development of the Papacy as both institution and theological dogma. It orients the Western church in a more ‘monarchic’ way than the Eastern church, which continues to practice a more collegial hierarchy. One example of this would be that when dealing with mission efforts among Slavs and Bulgars, the Western Catholics insisted Latin be the language of worship, whereas the Orthodox promoted the use of Slavic, translated both Scriptures and Liturgy, and established the Bulgarian church as a separate and independent hierarchical institution. It is simply and patently untrue to say, as another poster has, that E.Orthodoxy remains relatively unchanged since the 11th century. While there has probably been slightly less liturgical innovation in the Greek Orthodox churches than the Roman (especially with Vatican II), there has been plenty of theological development. I would not actually want to venture a proper answer to OP’s question, of whether the pre-Schism Western church was more similar to contemporary Roman Catholicism or contemporary Eastern Orthodoxy. It’s a no-win question that flattens the historical field in what I think is an inappropriate way

The answer is going to be a little infuriating. Simply the Western (roman rite) Church developed into the Roman Catholic and then Protestant sects. The Eastern Church developed into the Eastern Orthodox Church. The churches were functionally unique and autonomous well before the East-West Schism. The primary reason for the split was both cultural and political although there were some theological differences between the churches well before the official split in 1054. Possibly the biggest theological difference comes form this lingual and cultural difference. (I cited Pelikan, Jaroslav in my paper here but I can't seem to find a good online version of his work The Spirit of Eastern Christendom (600-1700)) The first big theological difference is know as fillique. Basicly the Roman Rite (I dont mean this in a conspiratorial way) inserted the phrase filique into the Latin recital of the Nicene Creed. This phrase means "and from the son." This is not in the Original Greek. The Catholic church has since removed this phrase from its greek recital of the the Creed although they stick behind their reasoning behind the phrase. (link 255 for a quick glimpse) This has been an area of major theological contention for quite some time with the earliest documented case of the insertion popping up in the latin coming from the the 6th century. Although this is phrased in my source (linked above) in such a way as to imply that this was because earlier records are gone rather than the 6th century was where the change originated from. Another area of difference is the idea of theoria versus metaphysics. Unfortunately my sources for this area are not up to snuff so I will save this for another poster to expand on.