This paper evaluates the use of various place-based and people-based measures of accessibility in the context of public service delivery. While place-based measures examine the spatial separation between service locations and in a single reference location, people-based measures are based on detailed observations of an individual's activity schedule and space–time constraints. The aim of this paper is to contribute to previous methodological studies of accessibility by investigating the extent to which utility-based measures relying on the Burns–Miller framework relate to place- based and other people-based measures of individual accessibility. In total, four place-based and six people-based measures that are frequently used to evaluate urban service delivery are analyzed. The relationships between these measures are examined and their implications for the assessment of equity of urban service distribution are evaluated. We have found substantial differences between place-based and people-based measures, supporting previous findings in the relevant literature and extending them to utility-based space–time measures of accessibility. We also observed substantial differences within the group of people-based measures. It appears that measures which express the cardinality of a feasible opportunity choice set are quite different from measures which express the desirability of such a set. The salience of this difference is also borne out by the measurement of statistical dispersion of accessibility values, indicating that different measures provide markedly different insights into how equally service delivery is distributed among the population.