It’s not even a question about which of the two is older — the “Roman” Catholic Church or the Eastern Orthodox Churches. It’s about the structure of the early Church. The Catholic Church acknowledges that the Eastern Orthodox have apostolic succession, hence they have a valid priesthood and valid Sacraments. You can’t have an older Church than the Catholic Church if like the Catholic Church your Church has apostolic succession.
The Sea of Peter in Rome leads the “Roman” Catholic Church and the Sea of Andrew in Constantinople leads the Eastern Orthodox Churches. They were once in full communion with each other. The Council of Chalcedon upheld the primacy of Old Rome (see Canon 28), even stating that New Rome — Constantinople — must “in ecclesiastical matters also be magnified as she is, and rank next after” Old Rome. It added, “The bishop of Constantinople however shall have the prerogative of honour next after the bishop of Rome”.
Saint Irenaeus mentions “the greatest and most ancient church” was “founded and organized at Rome by the two most glorious apostles” Peter and Paul (Against Heresies 3:3:2). The Eastern Orthodox haven’t even had an ecumenical council since before the Great Schism. It’s like they have been waiting for Rome because they know of Rome’s special place which is irreplaceable. For two thousand years Christians all over the world have submitted to the Holy See.