While there is a clear demand for scenarios that provide alternative states in biodiversity with respect to future emissions, a thorough analysis and communication of the associated uncertainties is still missing. Here, we modelled the global distribution of~11,500 amphibian, bird and mammal species and project their climatic suitability into the time horizon 2050 and 2070, while varying the input data used. By this, we explore the uncertainties originating from selecting species distribution models (SDMs), dispersal strategies, global circulation models (GCMs), and representative concentration pathways (RCPs). We demonstrate the overwhelming influence of SDMs and RCPs on future biodiversity projections, followed by dispersal strategies and GCMs. The relative importance of each component varies in space but also with the selected sensitivity metrics and with species' range size. Overall, this means using multiple SDMs, RCPs, dispersal assumptions and GCMs is a necessity in any biodiversity scenario assessment, to explicitly report associated uncertainties.