The extent of the savanna biome is expected to be profoundly altered by climatic change and increasing atmospheric CO2 concentrations. Contrasting projections are given when using different modelling approaches to estimate future distributions. Furthermore, biogeographic variation within savannas in plant function and structure is expected to lead to divergent responses to global change. Hence the use of a single model with a single savanna tree type will likely lead to biased projections. Here we compare and contrast projections of South American, African, and Australian savanna distributions from a physiologically-based statistical distribution model - the Thornley transport resistance model (TTR-SDM) - and three versions of a dynamic vegetation model (DVM) designed and parameterized separately for specific continents. We show that attempting to extrapolate any continent-specific model globally biases projections. By 2070 all DVMs generally project a decrease in the extent of savannas at their boundary with forests, whereas the TTR-SDM projects a decrease in savannas at their boundary with aridlands and grasslands. This difference is driven by forest and woodland expansion in response to rising atmospheric CO2 concentrations in DVMs, unaccounted for by the TTR-SDM. We suggest that the most suitable models of the savanna biome for future development are individual-based dynamic vegetation models designed for specific biogeographic regions.