This paper provides a comparative study between Inverse Reinforcement Learning (IRL) and Apprenticeship Learning (AL) reduced to classification. IRL and AL are two frameworks for the imitation learning problem where an agent tries to learn from demonstrations of an expert. In AL, the agent tries to learn the expert policy whereas in IRL, the agent tries to learn a reward which can explain the behavior of the expert. Then, the optimal policy regarding this reward is used to imitate the expert. One can wonder if it is worth estimating such a reward, or if estimating a policy is sufficient. This quite natural question has not really been addressed in the literature so far. We provide partial answers, both from a theoretical and empirical points of view.