Cooperative robots for intraocular surgery allow surgeons to perform vitreoretinal surgery with high precision and stability. Several robot structural designs have shown capabilities to perform these surgeries. This research investigates the comparative performance of a serial and parallel cooperative-controlled robot in completing a retinal vessel-following task, with a focus on human-robot interaction performance and user experience. Our results indicate that despite differences in robot structure and interaction forces and torques, the two robots exhibited similar levels of performance in terms of general robot-to-patient interaction and average operating time. These findings have implications for the development and implementation of surgical robotics, suggesting that both serial and parallel cooperative-controlled robots can be effective for vitreoretinal surgery tasks.