This is misleading. The Great Schism was not a simple case of one lone patriarch (the Pope) opposing four others of equal influence. By the 11th century, there was essentially the Latin Church and the Byzantine Church. The Patriarchs of Alexandria, Antioch, and Jerusalem were under the sway and shadow of Constantinople. The bulk of the original, ancient Churches of Alexandria and Antioch, the Coptic and Syriac Churches, had long since gone into schism with both Rome and Constantinople by this time (at the Council of Chalcedon five centuries earlier).
That being said, yes, I as a Catholic agree that the Eastern Patriarchs are the Pope’s peers. He holds primacy, but they are his brothers not his subjects. Cardinals hold great honour in the Church, elect the Pope of Rome, and exercise immense influence throughout the Catholic Church around the world, but ultimately they are officials of the Latin Church while Patriarchs head sister Churches “sui iuris” of equal dignity to the Latin Church.