This paper aims to analyse two energy storage methods—batteries and hydrogen storage technologies—that in some cases are treated as complementary technologies, but in other ones they are considered opposed technologies. A detailed technical description of each technology will allow to understand the evolution of batteries and hydrogen storage technologies: batteries looking for higher energy capacity and lower maintenance, while hydrogen storage technologies pursuing better volumetric and gravimetric densities. Additionally, as energy storage systems, a mathematical model is required to know the state of charge of the system. For this purpose, a mathematical model is proposed for conventional batteries, for compressed hydrogen tanks, for liquid hydrogen storage and for metal hydride tanks, which makes it possible to integrate energy storage systems into management strategies that aim to solve the energy balance in plants based on hybrid energy storage systems. From the technical point of view, most batteries are easier to operate and do not require special operating conditions, while hydrogen storage methods are currently functioning at the two extremes (high temperatures for metal and complex hydrides and low temperatures for liquid hydrogen or physisorption). Additionally, the technical comparison made in this paper also includes research trends and future possibilities in an attempt to help plan future policies.