The recent acceleration of global climate warming has created an urgent need for reliable projections of species distributions, widely used by natural resource managers. Such projections, however, are produced using various modeling approaches with little information on their relative performances under expected novel climatic conditions. Here, we hindcast the range shifts of five forest tree species across Europe over the last 12,000 years to compare the performance of three different types of species distribution models and determine the source of their robustness. We show that the performance of correlative models (CSDMs) decreases twice as fast as that of process-based models (PBMs) when climatic dissimilarity rises, and that PBM projections are likely to be more reliable than those made with CSDMs, at least until 2060 under scenario SSP245. These results demonstrate for the first time the well-established albeit so far untested idea that explicit description of mechanisms confers models robustness, and highlight a new avenue to improve model projections in the future.