Yes, Catholicism was like the Eastern Orthodox church. However, some would like to view it as it was not. I feel like it was at one point like the Eastern Orthodox church. They are both catholic and at some point branched away from each other and developed their own views towards things.
Rome was the center of the Catholic Church, while Byzantium (Constantinople) was the head of the Eastern Church in the first few hundred years of the Christian churches. The two had to be similar in scope until, like animals living on different continents, the churches drifted apart because different leaders had different ideological stances.
After all both the Roman Catholic and Eastern Orthodox Church are CATHOLIC and are descendant in the church of the Roman Empire that was the main church before the two split. I believe the variant of the Roman Catholic church in Latin America is much like what Catholicism used to be in the Middle Ages. It's only in the last few centuries that the Catholic church has become a little more Protestantized if you will as a result of the Counter Revolution. And I must say the stereotypes of Eastern Orthodox Catholics are pretty untrue. Many of the Eastern Orthodox people I know are very accepting of others, especially tomboys and autistic people. Same with Cubans.