We analyze the most important approaches for comparing the performance of hospitals: hospital cost functions, stochastic frontier analysis (SFA), and data envelopment analysis (DEA). Our analysis suggests that the strengths and weaknesses of these approaches differ by type of research or policy question and by the kind of data at hand. Parametric approaches including SFA are particularly useful when the research questions can be analyzed via aggregate output indicators. In addition these approaches are particularly good at analyzing hospital costs and performance in an episode specific manner. The non-parametric DEA in contrast facilitates to consider the great variety of inputs and outputs in a disaggregated form. However, for DEA results to be meaningfully interpretable, the hospitals under consideration need to be similar with regard to input and output categories as well as with regard to their production process. Furthermore, the DEA can only to a limited extent take account of the influence of exogenous environmental factors, modelling and data errors, and statistical outliers. It is therefore particularly useful when similar hospitals ought to be compared based on a high-quality data-set. Moreover, the paper illustrates that average and individual performance scores for hospital differ by type of approach selected, modeling and specification choices. We conclude the paper by outlining an approach that enables researchers and policy makers to deduct policy recommendations in the face of this uncertainty and by presenting recent methodological innovations for the outlined approaches.