How do traditionalists determine which tradition is correct?

Catholic and Eastern Orthodox theologians usually cite the authority of tradition in order to refute Protestants on any point where we have disagreement. Many Protestants also like to cite tradition; for instance, Luther and Calvin were adamant that they were not innovators, but simply returning to the doctrines of the ancient church which the Roman Catholics had drifted away from. However, Catholics and Eastern Orthodox point to institutional continuity and the idea of Apostolic Succession in order to argue that Protestant churches are not legitimate churches. Similar appeals to tradition and apostolic succession are made by the Oriental Orthodox Churches and the Assyrian Church of the East and other splinter groups. For the purposes of this question, "traditionalist" refers to those groups which emphasize the Sacred Tradition as an additional authority beside Scripture, and emphasize the institutional continuity back to the apostles. Thus the principle branches of traditionalists are the Roman Catholic Church, the Eastern Orthodox Church, the Oriental Orthodox Church, and the Assyrian Church of the East. These groups are all mutually not in communion with one another and have profound disagreements. **How do they discern which tradition is the correct tradition?** This is an *epistemological* question; while the particular disagreements among them are interesting and may serve as examples, I want to know by what methods traditionalists determine which tradition is correct. From my limited understanding, I see a lot of arguments that amount to begging the question. For instance, you might appeal to ecumenical councils, but how do you determine which councils are ecumenical? Only the First Council of Nicaea (325) and the First Council of Constantinople (381) are recognized by all four traditionalist branches. (And it would appear from reading Wikipedia's article that even within a particular tradition, there may be different opinions as to which councils are "ecumenical".) Or you might appeal to the authority of the Pope, but that is exactly the point at issue. How do you know that the tradition of following the Pope is the correct tradition?