Learning and matching a user’s preference is an essential aspect of achieving a productive collaboration in long-term Human-Robot Interaction (HRI). However, there are different techniques on how to match the behavior of a robot to a user’s preference. The robot can be adaptable so that a user can change the robot’s behavior to one’s need, or the robot can be adaptive and autonomously tries to match its behavior to the user’s preference. Both types might decrease the gap between a user’s preference and the actual system behavior. However, the Level of Automation (LoA) of the robot is different between both methods. Either the user controls the interaction, or the robot is in control. We present a study on the effects of different LoAs of a Socially Assistive Robot (SAR) on a user’s evaluation of the system in an exercising scenario. We implemented an online preference learning system and a user-adaptable system. We conducted a between-subject design study (adaptable robot vs. adaptive robot) with 40 subjects and report our quantitative and qualitative results. The results show that users evaluate the adaptive robots as more competent, warm, and report a higher alliance. Moreover, this increased alliance is significantly mediated by the perceived competence of the system. This result provides empirical evidence for the relation between the LoA of a system, the user’s perceived competence of the system, and the perceived alliance with it. Additionally, we provide evidence for a proof-of-concept that the chosen preference learning method (i.e., Double Thompson Sampling (DTS)) is suitable for online HRI.