Aggressive behaviour by dogs is a considerable social problem, but the ability to predict which individuals may have increased aggressive tendencies is very limited, restricting the development of efficient preventive measures. There is a common perception that certain breeds are more likely to exhibit aggressive behaviour, which has contributed to the introduction of breed‐specific legislation. The rationale for such legislation explicitly assumes high heritability of this trait while also implying relatively little variation within breeds; these assumptions are largely untested. We compared behavioural tendencies between 8 breeds that are subject to legislation in at least one country and 17 breeds that are not subject to legislation using two validated psychometric tools: the Dog Impulsivity Assessment Scale (DIAS), which scores elements of impulsivity, including a tendency for aggressive behaviour, and Positive and Negative Activation Scale (PANAS), which scores sensitivity to positive and negative stimuli (which may trigger aggressive responses). We found that the two groups of breeds do not differ significantly in the specific DIAS factor relating to aggressive behaviour, “Aggression Threshold and Response to Novelty”, or any other DIAS and PANAS factors. We found large variations in all behavioural tendencies measured by both psychometric scales within both groups and within each breed studied. Taken together, our findings indicate that breed alone is not a reliable predictor of individual behavioural tendencies, including those related to aggression, and therefore breed‐specific legislation is unlikely to be an effective instrument for reducing risk.