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Cognitive control refers to the ability of human beings to adapt flexibly and quickly to continuously changing environments. Several decades of research have identified a diverse range of mental processes that are associated with cognitive control but the extent to which shared systems underlie cognitive control in social and non-social contexts, as well as how these systems may vary across individuals, remains largely unexplored. By integrating methodological approaches from experimental and differential psychology, the current study is able to shine new light on the relationships between stable features of individuals, such as personality and sex, and the architecture of cognitive control systems using paradigms that index social (automatic imitation) and spatial processes. Across three large-sample experiments (>600 participants in total), we demonstrate that cognitive control systems are largely invariant to stable aspects of personality, but exhibit a sex difference, such that females show greater task-interference than males. Moreover, we further qualified this sex difference in two ways. First, we showed that the sex difference was unrelated to the sex of the interaction partner and therefore did not reflect an in-group bias based on sex. Second, we showed that the sex difference was tied to a form of spatial interference control rather than social (imitative) control and therefore it does not reflect a specialised mechanism for guiding social interactions exclusively. Instead, our findings suggest that a robust sex difference exists in the system (or set of subsystems) that operate in resolving a form of spatial interference control, and that such systems are unaffected by social factors such as the sex of the interaction partner. The results highlight the value of integrating approaches from experimental and differential psychology by providing a deeper understanding of the structure of cognitive control systems, whilst also providing new dimensions to incorporate into theories and models of social and non-social control.