The joint inversion of multiple data sets encompasses the advantages of different geophysical methods but may yield to conflicting solutions. Global search methods have been recently developed to address the issue of local minima found by derivative-based methods, to analyse the data compatibility and to find the set of trade-off solutions, since they are not unique. In this paper, we examine two evolutionary algorithms to solve the joint inversion of electrical and electromagnetic data. These nature-inspired metaheuristics also adopt the principle of Pareto optimality in order to identify the result among the feasible solutions and then infer the data compatibility. Since the joint inversion is characterized by more than one objective, we implemented the algorithm multi-objective particle swarm optimization (MOPSO) to jointly interpret time-domain electromagnetic data and vertical electrical sounding. We first tested MOPSO on a synthetic model. The performance of MOPSO was directly compared with that of a multi-objective genetic algorithm, the non-dominated sorting genetic algorithm (NSGA-III), which has often been adopted in geophysics. The adoption of MOPSO and NSGA-III enabled avoiding both simplification into a single-objective problem and the use of a weighting factor between the objectives. We tested the two methods on real data sets collected in the northwest of Italy. The results obtained from MOPSO and NSGA-III were highly comparable to each other and largely consistent with literature findings. The MOPSO performed a rigorous selection of the best trade-off solutions and its convergence was faster than NSGA-III. The analysis of the Pareto Front reported data incompatibility, which is very common for real data due to different resolutions, sensitivities and depth of investigations. Notwithstanding this, the multi-objective optimizers provided a complementary interpretation of the data, ensuring significant advantages with respect to the separate optimizations we carried out using the single-objective particle swarm optimization algorithm.