This paper aims to provide a novel insight into the influence of uncertainties in system- and pedestrian-induced load parameters on the vibration response of footbridges. The study begins with a sensitivity analysis for the vertical vibration response of a representative footbridge to two loading cases: a single pedestrian and a crowd. Two methods are utilized: the Sobol’-based global sensitivity analysis method and the local sensitivity analysis method. Uncertainties in all model parameters (which include bridge and human body dynamics in a walking posture, as well as dynamic force generated by humans) are considered in stochastic response estimation. Parametric analysis is then performed to investigate the influence of the variation of the mean values of the bridge modal mass, damping ratio, and natural frequency on the results of global and local sensitivity analysis. Systematic comparison of the results of global and local sensitivity analysis is performed to identify their similarities and differences. It has been found that the sensitive parameters and their importance ranking strongly depend on bridge modal properties and loading scenarios (i.e., a single pedestrian or a crowd crossing). The damping ratio and natural frequency of the human body are found to be the only two insensitive parameters. Therefore, they could be treated as deterministic parameters in the stochastic estimation of human-induced vibration. Global sensitivity analysis is recommended as a choice for the sensitivity analysis of pedestrian-induced vibration of footbridges as it leads to more reliable results, owing to the advantage of characterizing model sensitivity over the entire input spaces.