Roman Catholic Church and Eastern orthodox were not split back then, so they belong from that point to both. (And both canonised them as Saints). But their work contineued and trived in Eastern Chruch, while in West it was reduced to few tiny enclaves then. From that point they are more Orthodox (where their cult is stronger). Also, both were clierics of Eastern Chruch, an turned to finish their service in Western, but like I said, back then it was one Church.