A longstanding engineering ambition has been to design anthropomorphic bionic limbs: devices that look like and are controlled in the same way as the biological body (biomimetic). The untested assumption is that biomimetic motor control enhances device embodiment, learning, generalization, and automaticity. To test this, we compared biomimetic and non-biomimetic control strategies for able-bodied participants when learning to operate a wearable myoelectric bionic hand. We compared motor learning across days and behavioural tasks for two training groups: Biomimetic (mimicking the desired bionic hand gesture with biological hand) and Arbitrary control (mapping an unrelated biological hand gesture with the desired bionic gesture). For both trained groups, training improved bionic limb control, reduced cognitive reliance, and increased embodiment over the bionic hand. Biomimetic users had more intuitive and faster control early in training. Arbitrary users matched biomimetic performance later in training. Further, arbitrary users showed increased generalization to a novel control strategy. Collectively, our findings suggest that biomimetic and arbitrary control strategies provide different benefits. The optimal strategy is likely not strictly biomimetic, but rather a flexible strategy within the biomimetic to arbitrary spectrum, depending on the user, available training opportunities and user requirements.