Scholasticism was mainly promoted by the ideas of Thomas Aquinas. Aquinas, in turn, obtained most of his ideas from Aristotelian philosophy. Aquinas believed that Christianity could be rationally "proven" and that this could be done using the methods of reason, intellect and realism that were common in university environments, but that had rarely been used extensively within the Church. This approach gave great importance to philosophy, and attempted to reconcile this with faith.
On the other hand, Clairvaux was a proponent of mysticism. Mysticism focused on the spiritual matters of prayer, confession, forgiveness,and purpose. It also focused on personal development and on the pursuit of a life of sanctity.
I feel slightly more drawn towards scholasticism. I like the way it attempts to combine philosophy with religious thought. I also like the way in which reason and thought are included as part of a life of sanctity. However, I can see that scholasticism can have some problems when followed too closely. For a Christian, faith is important, and attempting to find a logical explanation for everything can diminish our faith, which should not question the wishes of God.
On the other hand, mysticism has certain strengths and weaknesses too. Its weaknesses can be found in the fact that mysticism focuses on the personal level. This might not be useful if we want establish general rules in the Church or want to focus on big questions. However, the advantage is that it allows for a very personal and unique experience for the individual.
