Great question. Those who follow Augustine tend to be less optimistic about humanity. They have a bleaker view of sin and the evils of humanity. They do not necessarily see progression in the human heart. They also believe that the mind is fallen to such an extent that it cannot reason its way to an understanding of God. This is why they believe that the coordination of faith and reason is that of faith seeking out reason. Many conservative Christians fall into this camp.
Those who follow Aquinas are more optimistic. They believe that you can argue and prove the existence of a Christian God. So, they see the coordination of faith and reason in the opposite way: they reason in order to have faith. In light of this, they are more embracing of the world and optimistic of secular engagement.