This paper presents a study on the impact of autonomy in the context of human-robot collaboration. We consider two conditions: i) a semi-autonomous robot that decides when to execute a supporting action, and ii) a support robot that has to be instructed of each action on a collaborative task. The semi-autonomous robot gradually learns how to support the human through experience. We found that users prefer the semi-autonomous robot and that the behavior was closer to their expectations despite them being more afraid of it. We also found that even if users noticed the robot was learning in one case, they wanted more autonomy in both conditions.