In artificial neural networks, acquiring new knowledge often interferes with existing knowledge. Here, although it is commonly claimed that humans overcome this challenge, we find surprisingly similar patterns of interference across both types of learner. When learning sequential rule-based tasks (A-B-A), both learners benefit more from prior knowledge when the tasks are similar-but as a result, they also exhibit greater interference when retested on task A. In networks, this arises from reusing previously learned representations, which accelerates new learning at the cost of overwriting prior knowledge. In humans, we also observe individual differences: one group ('lumpers') shows more interference alongside better transfer, while another ('splitters') avoids interference at the cost of worse transfer. These behavioural profiles are mirrored in neural networks trained in the rich (lumper) or lazy (splitter) regimes, encouraging overlapping or distinct representations respectively. Together, these findings reveal shared computational trade-offs between transferring knowledge and avoiding interference in humans and artificial neural networks.