Background: As the share of older adults worldwide increases, the supply of affordable and accessible health care may not match the pace with the growing demand. Thus, assistive care robots receive growing attention. However, while their potential is great in terms of preserving the patients’ sense of autonomy and meeting staff shortages, scepsis remains from a social science perspective. Care tasks often require close physical contact between caretaker and -receiver. This can be difficult, whether it is a human caregiver, or a robot. Notwithstanding that, everyone in need of care tends to hold different expectations, requirements, and prerequisites. Thus, acceptance issues might vary on the acceptance of assistive care robots and preference regarding who should handle which tasks. Objective: Using a quantitative empirical approach, we focused on identifying factors influencing assistive care robots’ acceptance. The overall aim was to understand the requirements of accepting robotic care assistance, comparing human vs. robotic assistance preferences in various caring tasks. Method: We used an online survey (N = 294) in which different Human-AI-Interaction-related scenarios and issues were investigated. In detail, we examined the locus of control (LoC), prior experience with care, gender, task delegation preferences, and acceptance of receiving care by a human versus a robot caretaker for various tasks. Results: The results reveal that care robots are equally well-received as their human counterparts. However, this changes considerably depending on the tasks at hand. The more intimate and shameful a task is considered, the more likely the robotic caretaker is preferred. Regarding user factors, gender and LoC showed to be impactful. Conclusion: The results of the present study offer insights into the current state of user acceptance of assistive robots in the health care sector. Moreover, they shall help identify tasks for which such robots can provide the most significant benefit for those in need of care. Overall, assistive care robots seem to be best suited as supplementary caregivers rather than a complete substitute. Although they were generally perceived positively, this assessment was task- and user-dependent.