The assessment of return periods of extreme hydrological events often relies on statistical analysis using generalized extreme value (GEV) distributions. Here we compare the traditional GEV approach with a novel large ensemble approach to determine the added value of a direct, empirical distribution‐based estimate of extreme hydrological events. Using the global climate and hydrological models EC‐Earth and PCR‐GLOBWB, we simulate 2,000 years of global hydrology for a present‐day and 2 °C warmer climate. We show that the GEV method has inherent limitations in estimating changes in hydrological extremes, especially for compound hydrological events. The large ensemble method does not suffer from these limitations and quantifies the impacts of climate change with greater precision. The explicit simulation of extreme events enables better hydrological process understanding. We conclude that future studies focusing on the impact of climatic changes on hydrological extremes should use large ensemble techniques to properly account for these rare hydrological events. Plain Language Summary: Extreme hydrological events such as droughts and floods can cause severe harm to people and nature. It is therefore important to understand why and how often they occur now and in the future. We compare two methods of studying these extreme events: a frequently used statistical method and a new direct simulation method (called "large ensemble simulations"). We show that this new method better represents the extreme events, that it reduces the uncertainties of the expected effects of climate changes on extreme events, and that it allows us to study why extreme events occur. We therefore are better capable to quantify the impact of climate change on hydrological extremes, and we recommend the large ensemble method for future studies on extreme events. Key Points: Statistical models to describe extreme river discharge can be unreliable when multiple processes lead to extreme eventsLarge ensemble model experiments (many simulation years) are suitable for analysis of extreme events and do not rely on statistical modelsHydrological large ensembles provide better estimates of changes in extreme floods and droughts and their characteristics [ABSTRACT FROM AUTHOR]