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Anti-NASICON Fe2(MoO4)3 (P21/c) shows significant structural and electrochemical differences in the intercalation of Li+ and Na+ ions. To understand the origin of this behavior, we have used a combination of in-situ X-ray and high-resolution neutron diffraction, total scattering, electrochemical measurements, density functional theory calculations, and symmetry-mode analysis. We find that for Li+-intercalation, which proceeds via a two-phase monoclinic-to-orthorhombic (Pbcn) phase transition, the host lattice undergoes a concerted rotation of rigid polyhedral subunits driven by strong interactions with the Li+ ions, leading to an ordered lithium arrangement. Na+- intercalation, which proceeds via a two-stage solid solution insertion into the monoclinic structure, similarly produces rotations of the lattice polyhedral subunits. However, using a combination of total neutron scattering data and density-functional theory calculations, we find that while these rotational distortions upon Na+ intercalation are fundamentally the same as for Li+ intercalation, they result in a far less coherent final structure, with this difference attributed to the substantial difference between the ionic radii of the two alkali metals.