Renewable energy resources, such as wind and solar, have been applied throughout the world on a large scale, taking advantage of existing potential and gradual cost reduction to finally meet global decarbonization targets. However, the intermittent characteristic of most of these resources usually culminates in energy planning with a large installed capacity to meet high-end energy dispatch. The consequence is an inefficient power grid and the adoption of power generation curtailments during low demand periods. Therefore, the penetration of intermittent renewable energy sources into power grids must be accompanied by a significant increase in their energy storage capacity. The analysis presented in this paper considers two large scale energy storage alternatives: Pump Hydro Storage (PHS) and Hydrogen (H2). For the PHS case, data of existing and potential plants were used as a reference, assuming that the same amount of pumped energy will be re-electrified afterward. It was also assumed that the same amount of energy available to be pumped by PHS, is electrically available to be stored as H2. The electrolysis process was considered for H2 production, and the power recovery (re-electrification) was assumed to be executed by H2 burning using modern gas turbines. Energy and exergy analyses for PHS and H2 alternatives were performed, efficiency results are presented, and finally a significant advantage for PHS is observed.