In this paper, a comparison between a “pure” genetic algorithm (GeDEA-II) and a surrogate-assisted algorithm (ASEMOO) is carried out using up-to-date multiobjective and multidimensional test functions. The experimental results show that the use of surrogates greatly improves convergence when both two- and three-objective test cases are dealt with. However, its convergence capabilities depend on how the surrogate can have an accurate picture of the fitness function landscape and seem to decrease as the number of the objective increases from two to three. On the other hand, a pure genetic algorithm always assures a minimum level of “front coverage”, regardless of the problem on hand. Such minimum level could be considered sufficient for real-life problem optimizations. Also The dimensionality of the design space affects in opposite directions the two algorithms: for ASEMOO the increase of dimensionality is detrimental on performance, while GeDEA-II experiences benefits due to total amount of direct evaluations. It seems that GeDEA-II has an optimal population size around 20, regardless the dimensionality of the problem at hand.