In hydrological studies models with a fixed structure are commonly used. For various reasons, these models do not always perform well. As an alternative, a flexible modelling approach could be followed, where the identification of the model structure is part of the model set-up procedure. In this study, the performance of twelve different conceptual model structures from the SUPERFLEX framework with varying complexity and the fixed model structure of GR4H were compared on a large set of 237 French catchments. The results showed that in general the flexible approach performs better than the fixed approach. However, the flexible approach has a higher chance of inconsistent results when implemented on two different periods. The same holds for more complex model structures. When for practical reasons a fixed model structure is preferred, this study shows that models with parallel reservoirs and a power function to describe the reservoir outflow perform best. In general, conceptual hydrological models perform better on large or wet catchments than on small or dry catchments. The model structures performed poorly when there was a climatic difference between the calibration and validation period, for catchments with flashy flows or disturbances in low flow measurements.