The council of Ephesus basically used the Christology of the School of Alexandria against Nestorius, a person who held to an extremist interpretation of the theology of the school of Antioch. Since the Antiochan school emphasized the humanity of Christ, Nestorius went to the extreme and denied the title of Theotokos for the Virgin Mary (and thus claimed 2 hypostasis for Christ). At the Council of Ephesus, the Antiochan delegation arrived late and were angered that St Cyril started the council and its condemnation of Nestorius, one of their fellow kinsman.
Ephesus didnt become truly ecumenical until 2 years later when Patriarch John of Antioch and St. Cyril of Alexandria reconciled in the "formula of reunion". Basically both sides accepted each others Christology, Cyril accepted the Antiochan Tradition concerning the Two natures and John of Antioch accepted the condemnation of Nestorius and fully recieved the dogma of the 'Theotokos'.
In Chalcedon, it was time for the Christology of the Antiochan School to step up and condemn the teaching of Eutyches, which was an extremist interpretation of the Christology of the Alexandrian School ,which emphasized the divinity of Christ. Eutyches basically fell into heresy because of his zeal to persecute the last remaining Nestorians of Constantinople. Thus he created a heretical extremist Christology of monophysitism to counter anything the Nestorians produced.
While Pope Leo's tome taught the two natures, the definition of Chalcedon is not based entirely on it. Its basically Antiochan Christology.