Future climate change has the potential to increase drought in many regions of the globe, making it essential that land surface models (LSMs) used in coupled climate models realistically capture the drought responses of vegetation. Recent data syntheses show that drought sensitivity varies considerably among plants from different climate zones, but state-of-the-art LSMs currently assume the same drought sensitivity for all vegetation. We tested whether variable drought sensitivities are needed to explain the observed large-scale patterns of drought impact on the carbon, water and energy fluxes. We implemented data-driven drought sensitivities in the Community Atmosphere Biosphere Land Exchange (CABLE) LSM and evaluated alternative sensitivities across a latitudinal gradient in Europe during the 2003 heatwave. The model predicted an overly abrupt onset of drought unless average soil water potential was calculated with dynamic weighting across soil layers. We found that high drought sensitivity at the most mesic sites, and low drought sensitivity at the most xeric sites, was necessary to accurately model responses during drought. Our results indicate that LSMs will over-estimate drought impacts in drier climates unless different sensitivity of vegetation to drought is taken into account.