We investigate whether a robot should behave as a collaborator or as a cooperator of a human partner in a comanipulation task. In a previous study, we addressed the same question for a human-human dyad and found that collaboration is preferable to make fewer errors at the expense of increased arm stiffness for the humans, who behave as if they were both leaders. In this study, the human is coupled with a Franka robot and they jointly engage in the same co-manipulation task in different conditions. In the cooperation conditions, the robot is either a leader or a follower, exhibiting fixed impedance strategies. In the collaborative conditions, the robot exhibits either reciprocal or mirrored adaptive impedance strategies that vary according to an EMG-based online estimation of the human arm stiffness. Our results show that, for the co-manipulation task, a robot collaborator seems more preferable than a robot cooperator, leader or follower, and that the reciprocal strategy for impedance seems to be the most indicated.