Mechanistic models simulate the habitat preferences and foraging behaviour of pollinators, while data-driven models associate georeferenced variables with real observations. Here, we test these two approaches to predict pollination supply and validate these predictions using data from a newly released global dataset on pollinator visitation rates to different crops. We use one of the most extensively used models for the mechanistic approach, while for the data-driven approach, we select from among a comprehensive set of state-of-the-art machine-learning models. Moreover, we explore a mixed approach, where data-derived inputs, rather than expert assessment, inform the mechanistic model. We find that, at a global scale, machine-learning models work best, offering a rank correlation coefficient between predictions and observations of pollinator visitation rates of 0.56. In turn, the mechanistic model works moderately well at a global scale for wild bees other than bumblebees. Biomes characterized by temperate or Mediterranean forests show a better agreement between mechanistic model predictions and observations, probably due to more comprehensive ecological knowledge and therefore better parameterization of input variables for these biomes. This study highlights the challenges of transferring input variables across multiple biomes, as expected given the different composition of species in different biomes. Our results provide clear guidance on which pollination supply models perform best at different spatial scales – the first step towards bridging the stakeholder–academia gap in modelling ecosystem service delivery under ecological intensification.