Models with a fixed structure are widely used in hydrological studies and operational applications. For various reasons, these models do not always perform well. As an alternative, flexible modelling approaches allow the identification and refinement of the model structure as part of the modelling process. In this study, twelve different conceptual model structures from the SUPERFLEX framework are compared with the fixed model structure GR4H, using a large set of 237 French catchments and discharge-based performance metrics. The results show that, in general, the flexible approach performs better than the fixed approach. However, the flexible approach has a higher chance of inconsistent results when calibrated on two different periods. When analysing the subset of 116 catchments where the two approaches produce consistent performance over multiple time periods, their average performance relative to each other is almost equivalent. From the point of view of developing a well-performing fixed model structure, the findings favour models with parallel reservoirs and a power function to describe the reservoir outflow. In general, conceptual hydrological models perform better on larger and/or wetter catchments than on smaller and/or drier catchments. The model structures performed poorly when there were large climatic differences between the calibration and validation periods, in catchments with flashy flows, and in catchments with unexplained variations in low flow measurements.