This work investigates the role of elastic coherency constraints in solute intercalation processes within metallic lattices, particularly in nanoscopic particles, and their impact on absorption and desorption kinetics in metal hydrides, involving coupled solute diffusion and phase transformations. This problem is of significant relevance to energy storage technologies, including hydrogen storage systems and lithium-ion batteries. Elastic coherency is identified as a primary mechanism governing phase transformation kinetics at the nanoscale (\cite{Cahn, Schwarz}). The specific system analyzed in this study is palladium–hydrogen (Pd–H) (\cite{Schwarz2, Weissmuller}). Two theoretical modeling frameworks are considered (cf. \cite{Fratzl}): (i) macroscopic models, in which the two phases undergoing transformation are treated as elastic continua separated by a sharp interface (sharp-interface models), as developed in \cite{Souza, Duda, Naele}; and (ii) mesoscopic models, in which the solute concentration varies smoothly across the interface and phase separation is described using a phase-field (diffuse-interface) formulation. In the latter case, the mesoscopic elastic free-energy contribution of the phase mixture is derived through a convexification procedure. The absorption–desorption kinetics are analyzed within both frameworks, with particular emphasis on the influence of coherency strain on the binodal and spinodal diagrams, as well as on the emergence of the elastic energy barrier that gives rise to hysteresis. Results obtained from the sharp-interface and diffuse-interface models are systematically compared, highlighting their respective capabilities and limitations in capturing the coupled chemo-mechanical effects governing phase transformation in metal hydrides. As a specific contribution of this work, a thermodynamically consistent continuum mechanics–based formulations underlying both modeling approaches are systematically derived and analyzed.