A multicriteria algorithm, the MultiObjective Generalized Sensitivity Analysis (MOGSA), was used to investigate the parameter sensitivity of five different land surface models with increasing levels of complexity in the physical representation of the vegetation (BUCKET, CHASM, BATS 1, Noah, and BATS 2) at five different sites representing crop land/pasture, grassland, rain forest, cropland, and semidesert areas. The methodology allows for the inclusion of parameter interaction and does not require assumptions of independence between parameters, while at the same time allowing for the ranking of several single-criterion and a global multicriteria sensitivity indices. The analysis required on the order of 50 thousand model runs. The results confirm that parameters with similar “physical meaning” across different model structures behave in different ways depending on the model and the locations. It is also shown that after a certain level an increase in model structure complexity does not necessarily lead to better parameter identifiability, i.e., higher sensitivity, and that a certain level of overparameterization is observed. For the case of the BATS 1 and BATS 2 models, with essentially the same model structure but a more sophisticated vegetation model, paradoxically, the effect on parameter sensitivity is mainly reflected in the sensitivity of the soil-related parameters.