Cyprianic vs. Augustinian?

Please do not take this as a scholarly piece in the least bit. Just a little of my own personal reflections. Many times there is considered a vast difference between the Sacramental theology of the Byzantine east vs. the theology of the Latin west. This, from my own observations, is root in a perceived difference in the teachings of St. Augustine and St. Cyprian. Supposedly at least. Its interesting because St. Cyprian and St. Augustine were both north Africans, and consequently both Latin culturally. They both even wrote in Latin as far as I know. So why the difference? To give a break down in the Augustinian(and later thomist view) a Sacrament needs several things
1. proper form
2. Proper matter
3. Intention to do what the Church does

Say for instance, the Eucharist. In the west, a priest who has valid orders can consecrete the Eucharist irrelevant of his faith in it or in the Church. Because intention is assumed if he is performing with proper matter and form.

In the Byzantine Orthodox east, there is no distinction between illicit and invalid. They need
1. Proper matter
2. Proper form
3. the Faith of the Church

So when a priest does proper form and matter in the Orthodox church, if he is not Orthodox then its irrelevant as he no longer posses the ability to celebrate the Mysteries at all! This is why some Orthodox rebaptize Catholics.

So if we look at these, perhaps there is a compromise that keeps both traditions intact fully. The intention to do as the Church does, and the faith of the Church really should be considered one in the same thing. I beleive, in my opinion, that the west has erred in some regard to this. Such as in the case of vagrant bishops who receive their orders from Old Catholics. Can such people so far from the Church structure really be intending to do as the Church intends? This automatic assumption on the part of the west of intention is ill founded. Likewise though, with the Orthodox. In the case of say , Catholic Sacraments. While there are serious disagreements between latins and the Orthodox on the role of the papacy, does that constitute a complete abandonment of the necessities of Orthodox faith for the celebration of the Mysteries? Just some thoughts I had.

(Excuse me my Orthodox readers if I have any, for talking of the mysteries in this very legalistic manner. I only am hoping to enlighten those unfamiliar with them. )