Data assimilation is a relevant framework to merge a dynamical model with noisy observations. When various models are in competition, the question is to find the model that best matches the observations. This matching can be measured by using the model evidence, defined by the likelihood of the observations given the model. This study explores the performance of model selection based on model evidence computed using data-driven data assimilation, where dynamical models are emulated using machine learning methods. In this work, the methodology is tested with the three-variable Lorenz' model and with an intermediate complexity atmospheric general circulation model (a.k.a. the SPEEDY model). Numerical experiments show that the data-driven implementation of the model selection algorithm performs as well as the one that uses the dynamical model. The technique is able of selecting the best model among a set of possible models and also to characterize the spatio-temporal variability of the model sensitivity. Moreover, the technique is sensitive to differences in the model dynamics which are not reflected in the moments of the climatological probability distribution of the state variables. This suggests the implementation of this technique using available long-term observations and model simulations.