Crop diseases and pests constitute significant causes of yield losses for crops. To limit the harm incurred by those events, farmers resort to plant protection products. Such products are known to have adverse effects both on the environment and on human health. Agronomists make continuous efforts to limit the usage of plant protection products to situations where those products are strictly necessary. To determine such situations, agronomists and policy-makers often rely on decision support tools to model and predict the dynamics of plant diseases. Decision support tools are based either on mechanistic models or on statistical approaches learned from large datasets of biotic (e.g., disease incidence, plant phenological stage) and abiotic (meteorological, soil characteristics) observations in cultures. The surge of powerful machine learning (ML) methods in the last decade makes such approaches a natural pathway to model the dynamics of plant diseases. Machine learning models can reveal the factors that contribute the most to disease and pests outbreaks, provided that those models are simple enough for human inspection. Simplicity, however, may come at the price of lower prediction performances when compared to more complex models. In this paper, we offer a deep look at the performance of ML models of different complexity when used on two use cases of crop disease prediction: downy mildew in the grapevine, and Cercospora leaf spot in the sugar beet. We compare model accuracy and complexity using a year-based cross-validation approach. Our results suggest that interannual meteorological variations are a very important factor in plant disease prediction. Moreover, in line with the observations of the research community in interpretable ML, model complexity stands in clear trade-off with accuracy. This makes models of intermediate complexity appealing for predicting the dynamics of crop diseases as they can provide explicit insights about the rationale of their predictions.