Two nonparametric methods for the identification of subgroups with outstanding outcome values are described and compared to each other in a simulation study and an application to clinical data. The Patient Rule Induction Method (PRIM) searches for box-shaped areas in the given data which exceed a minimal size and average outcome. This is achieved via a combination of iterative peeling and pasting steps, where small fractions of the data are removed or added to the current box. As an alternative, Classification and Regression Trees (CART) prediction models perform sequential binary splits of the data to produce subsets which can be interpreted as subgroups of heterogeneous outcome. PRIM and CART were compared in a simulation study to investigate their strengths and weaknesses under various data settings, taking different performance measures into account. PRIM was shown to be superior in rather complex settings such as those with few observations, a smaller signal-to-noise ratio, and more than one subgroup. CART showed the best performance in simpler situations. A practical application of the two methods was illustrated using a clinical data set. For this application, both methods produced similar results but the higher amount of user involvement of PRIM became apparent. PRIM can be flexibly tuned by the user, whereas CART, although simpler to implement, is rather static.