Sustainable development in degraded landscapes in the humid tropics require effective soil and water management practices. Coupled hydrological‐erosion models have been used to understand and predict the underlying processes at watershed scale and the effect of human interventions. One prominent tool is the parameter‐efficient distributed (PED) model, which improves on other models by considering a saturation‐excess runoff generation driving erosion and sediment transport in humid climates. This model has been widely applied at different scales for the humid monsoonal climate of the Ethiopian Highlands, with good success in estimating discharge and sediment concentrations. However, previous studies performed manual calibration of the involved parameters without reporting sensitivity analyses or assessing equifinality. The aim of this article is to provide a multi‐objective global sensitivity analysis of the PED model using automatic random sampling implemented in the SAFE Toolbox. We find that relative parameter sensitivity depends greatly on the purpose of model application and the outcomes used for its evaluation. Five of the 13 PED model parameters are insensitive for improving model performance. Additionally, associating behavioural parameter values with a clear physical meaning provides slightly better results and helps interpretation. Lastly, good performance in one module does not translate directly into good performance in the other module. We interpret these results in terms of the represented hydrological and erosion processes and recommend field data to inform model calibration and validation, potentially improving land degradation understanding and prediction and supporting decision‐making for soil and water conservation strategies in degraded humid landscapes.