Which older, the Catholic or the Orthodox church?

Neither. The Church founded by Christ was one for 1000 years. It split in two in the Great Schism of 1054. The bishop of Rome became the first Catholic pope, and the four remaining Christian bishops -- Alexandria, Antioch, Constantinople, and Jerusalem -- continued as authorities in the newly-named Eastern Orthodox Christian Church. Both Churches have apostolic succession, the Fullness of Truth, and all the Sacraments. Both worship only Father, Son, and Holy Spirit.

Assuming that you are referring specifically to the Roman Catholic Church and the Eastern Orthodox Church...

...that depends ENTIRELY on one's interpretation of the historical facts.

Roman Catholics claim that the Roman Catholic Church is the older and that the Eastern Orthodox Church was the "break away" church.

Eastern Orthodox claim that the Eastern Orthodox Church (which, by the way, has in Greek the title "Orthodox Catholic Church") is the older and that the Roman Catholic Church was the "break away" church.

In my opinion, which I believe to be objective, both churches are the direct hierarchical descendant of an earlier unified "catholic church". One church split into two, and neither of those two is the same church as the church from which they descended. Both teach doctrines significantly different than did that united church, and indeed the early differences in doctrine are the primary cause of that division.

They are of equal age.

The Catholic Church was founded 33 AD. The orthodox abandoned Christianity a thousand years later.

one and the same until all of the popes in all of the counries decided that each was better than the other

Orthodox

The Orthodox Church was headed by the Byzantine Emperor both before and after the Great Schism.

Both churches have heretic doctrines of men not taught in the New Testament.

Catholic and orthodox are both fake, they both lie about the Bible, they both contradict the Bible and the Gospel of Jesus Christ. Which is older makes no difference at all. They both lead to eternal torment in the lake of fire, so avoid both.

The truth is that Jesus is God! Jesus loves you! Death leads to immediate heaven or hell, and it is too late to be saved, after death. The only way to heaven is by believing in Jesus. The truth is that believing in Jesus to take you to heaven apart from any of your works, is the only way to heaven. Jesus paid it all, so believe in Jesus, and you're saved. There is no chance to be saved after death. Jesus Christ is God, Jesus died on the cross to pay for all of our sins, all sins past and future, to make all our sins forgiven, past and future, and then Jesus resurrected from the dead. Nothing else pays for our sins, not works or deeds or religions or anything. You cannot add any works to salvation (Romans 4:5). So to be in heaven and not in eternal torment in the lake of fire, believe in Jesus Christ to take you to heaven. That easy! Tell Jesus right now that you believe in Jesus for eternal life, and you will be in heaven! Jesus loves you and wants to bless you now and throughout your life and forever!..

Both churches were formed during the Great Schism. There is no name for the original church.

Of course, each church claims it was the original.

Catholic and Orthodox were formed about the same time.