Accurate estimation of baseflow and discharge is critical for sustainable water resource planning, particularly in tropical catchments with limited data quality. This study evaluated the sensitivity, uncertainty, and multi-objective performance of the WetSpass-M model in the Akaki catchment and its sub-catchments (Legedadi and Gefersa) in the central highlands of Ethiopia. The model incorporates meteorological, physiographic, and groundwater data. By varying the model parameters and using two potential evapotranspiration (PET) datasets—FAO Penman–Monteith (S1) and GLEAM (S2)—a total of 78 simulations were conducted, followed by one-at-a-time (OAT) sensitivity and uncertainty analyses. The results indicate that the runoff delay factor (X) is the most sensitive parameter across all sites, whereas the recharge contributing factor (∅) and soil moisture parameter (LP) have a moderate influence. In Akaki, GLEAM (S2) overestimated the baseflow more than FAO Penman–Monteith (S1). Legedadi predominantly overestimated baseflow, whereas Gefersa showed more variable and inconsistent responses. In both the catchment and sub-catchments, the discharge uncertainty was lower than the baseflow uncertainty. Multi-objective performance analysis further revealed that in Akaki, S1 generally outperformed S2 in baseflow prediction, whereas sub-catchment scale simulations demonstrated low model performance, particularly in Legedadi, highlighting the need for localized calibration-verification and high-quality observed data. Overall, the study underscores the critical role of PET dataset selection and model parameterization in hydrological modeling and highlights the need for comprehensive sensitivity and uncertainty analyses to improve model reliability and support informed water management decisions in rapidly urbanizing catchments.