This is a question that lacks a simple answer. Note that "Catholic" and "Orthodox" are terms that only really describe the churches after the great schism of 1054: prior to this time, they would have been viewed as one church accepting the doctrines laid out at Nicaea and Chalcedon (from whence "Chalcedonian"), though nonetheless cracks were starting to form.

Historically, the Pope had been viewed by Christians as the rightful successor to St. Peter, but he was not regarded as the head of the church or as having authority over all other bishops (the highest level of authority lay with the Ecumenical Patriarch in Constantinople). This began to change in the 7th and 8th centuries due to the growing rift between the Eastern Roman Empire, which had adopted Greek as its national language, and the Western "barbarians", whose lingua franca (so to speak) and liturgical language was Latin. The Easterners had always tried to retain some control over former Western territory, with varying degrees of success. Charlemagne's crowning as "Emperor of the Romans" by Pope Leo III deepened the rift between Greek East and Latin West; the Pope began to take a much more primary role in Western Christianity, not least because Westerners were more likely to speak Latin and because Rome was much closer than Constantinople. So it really is not surprising that Western kingdoms were warmer to "Latin" Christianity (which became Catholicism) than to "Greek" Christianity (which became Orthodoxy).

Note that the status of Catholicism as "dominant" is a bit of an oversimplification, though. Many Eastern European lands became and remained Orthodox, most notably Russia (with Moscow having been considered by some as "the third Rome" after the fall of Constantinople). Note, also, that the "dominance" of the ERE is an oversimplification, too. It lost significant land very quickly to the spread of Islam, but it was also constantly plagued by internal power struggles that limited its ability to project power beyond its borders.

One controversial issue surrounds the role of Hesychasm, a mystical movement in the Orthodox church that became dominant in Constantinople in the 14th century. At this time, scholastic and humanist traditions were increasingly becoming cemented in Western thought, not least because Catholics were eager to get their hands on classical Greek wisdom (exported by Orthodox scholars seeking to preserve classical knowledge; some of these scholars ended up converting to Catholicism). Interpreted one way, Hesychasm might have strongly weakened the chance of a reconciliation between East and West and therefore have been a contributing factor to the fall of Constantinople (which might have been staved off with stronger Western assistance), limiting the impact of Orthodox Christianity.

edit: I imagine you're looking for some deep fundamental difference between Catholicism and Orthodoxy that explains why the former dominated. There probably isn't one. Indeed, at the time of the schism the theological differences between them were fairly minor, though the political and cultural differences were not.