Summary: In the last decades, various frontier-based efficiency measurement methods have been developed. So far, there is only limited knowledge with respect to the question to what extent a certain method is advantageous in different scenarios. We address this issue by a simulation study. In the respective scenarios, nine parameters are varied that reflect the specific structure of the data and knowledge about the competitive environment of the units to be evaluated. In contrast to other studies, we consider, e.g., multiple inputs and outputs. Furthermore, among other things, we assume lower levels of efficiency to reflect characteristics of markets with weaker competition. The methods compared are Data Envelopment Analysis, Stochastic Frontier Analysis, Stochastic Non-Smooth Envelopment of Data, and Normalized Additive Analysis. They are assessed with respect to two main purposes of efficiency measurement, the correct estimation of the efficiency degrees as well as the accurate determination of the ranking of the compared units. It is shown that, depending on the chosen purpose and the data scenario, there are major differences regarding the performance of the methods. The results of our study provide a comprehensive basis for selecting between the methods.