Subservience.

The Nuns Story is a film in which Audrey Hepburn starred as a young women becoming a Postulate in preparation to entering the Catholic Church as a Nun.

The stricture of the church and the exclusion from worldly goods, even the strict silence which is introduced to subvert and focus the individual in the worship of God was starkly contrasted as the young girls said goodbye to their parents, parents who were confused by the apparent down grading of their deep parental love for an even deeper love, a love based on a concept which many would challenge.
Self denial is at the crux for many who wish to enter this sanctum. 

The mystic who reduces his belongings and seeks through meditation and denial of any worldly goods, is another manifestation of the search for clarity in self analysis, analysis which only withdrawal brings and allows the individual a different perspective on life. 

The Buddhist who undertakes a lifetime of analysis through contemplation to understand their position in the cycle of life and ultimately themselves in an attempt to come to terms with impermanence.
At the base of this is perhaps the inability to be satisfied with the human condition, the wish to intellectualise our condition because the simple fact that "we are born and we die" we "do good and bad" in equal proportion, is not good enough. Our brains must concoct a complexity of purpose which leads us into a labyrinth of uncertainty
There does seem to be at least one difference. The religious trail bows to the weight of gods ordinance whilst in the latter there is no hierarchy, only an attempt to understand ones own human frailty.