Despite its successes, to date Artificial Intelligence (AI) is still characterized by a number of shortcomings with regards to different application domains and goals. These limitations are arguably both conceptual (e.g., related to underlying theoretical models, such as symbolic vs. connectionist), and operational (e.g., related to robustness and ability to generalize). Biologically inspired AI, and more specifically brain-inspired AI, promises to provide further biological aspects beyond those that are already traditionally included in AI, making it possible to assess and possibly overcome some of its present shortcomings. This article examines some conceptual, technical, and ethical issues raised by the development and use of brain-inspired AI. Against this background, the paper asks whether there is anything ethically unique about brain-inspired AI. The aim of the paper is to introduce a method that has a heuristic nature and that can be applied to identify and address the ethical issues arising from brain-inspired AI. The conclusion resulting from the application of this method is that, compared to traditional AI, brain-inspired AI raises new foundational ethical issues and some new practical ethical issues, and exacerbates some of the issues raised by traditional AI.