The answer
The main difference in St. Cyril's Liturgy than in the other two is the order of the litanies. In St. Basil's Liturgy and in St. Gregory's Liturgy, the litanies come immediately after the epiclesis (the change of the elements to the Body and the Blood of the Lord), but in St. Cyril's Liturgy, the litanies precede the epiclesis. This reflects two schools of thought.In the Coptic mind (St. Cyril), they want to finish all the litanies before the change occurs; then after the change, all the focus is on praising the Lord ONLY.
In the Byzantine mind (St. Basil and St. Gregory), they want to present all their requests to the Lord after the change occurs because of the importance of these petitions.
No one approach is better than the other. It is just two schools of mind.
Answered by His Eminence Metropolitan Youssef (opens in a new tab)