Both becoming a friar and becoming a deacon involve taking an exam. The friar's exam is considerably easier and is the only one open to villeins, but being a friar and being a priest are even in Hyperion two different kinds of commitments.

For now, those taking the priest exam can become priests, but this is only because we need people to fulfill the roles of the first priests. Later, the exam will only allow you to become a deacon - acquisition of holy powers and the ability to demonstrate them is the second part of becoming a priest.

The roles of a priest and a friar are very different, however, both have appeal. Priests generally occupy different roles on the battlefield than friars, who after all may still be normal enlisted footmen in the military. Priests also are the ones who are in charge of churches, even if they are alone in their village church - whereas a friar is always guaranteed a community. Even a noble knight who wishes to join the clergy may elect to join as a friar rather than becoming ordained as a priest, so even though a friar is ranked lower in the church heirarchy than a priest, it really amounts to the type of playstyle you desire.