Solving very-large-scale optimization problems frequently require to decompose them in smaller subproblems, which are iteratively solved to produce useful information. One such approach is the Lagrangian relaxation (LR), a general technique that leads to many different decomposition schemes. The LR produces a lower bound of the objective function and useful information for heuristics aimed at constructing feasible primal solutions. In this paper, we compare the main LR strategies used so far for stochastic hydrothermal unit commitment problems, where uncertainty mainly concerns water availability in reservoirs and demand (weather conditions). The problem is customarily modeled as a two-stage mixed-integer optimization problem. We compare different decomposition strategies (unit and scenario schemes) in terms of quality of produced lower bound and running time. The schemes are assessed with various hydrothermal systems, considering different configuration of power plants, in terms of capacity and number of units.