CO2 hydrogenation toward methane, a reaction of high environmental and sustainable energy importance, was investigated at 200–600 °C and H2/CO2 = 4/1, over Rh nanoparticles dispersed on supports with different oxygen storage capacity characteristics (γ-Al2O3, alumina-ceria-zirconia, and ceria-zirconia). The effects of the support OSC and Rh particle size on reaction behavior under both integral and differential conditions were investigated, to elucidate the combined role of these crucial catalyst design parameters on methanation efficiency. A volcano-type variation of methanation turnover frequency was found in respect to support OSC; Rh/ACZ, with intermediate OSC, was the optimal catalyst. The structure sensitivity of the reaction was found to be a combined function of support OSC and Rh particle size: For Rh/γ-Al2O3 (lack of OSC) methanation was strongly favored on small particles—the opposite for Rh/CZ (high OSC). The findings are promising for rational design and optimization of CO2 methanation catalysts by tailoring the aforementioned characteristics.