Lignin depolymerization through peroxide oxidation produces dicarboxylic acids (DCA), especially C-4-DCA, like succinic acid. In this work, the effect of methoxy substituents on C-4-DCA production using peroxide oxidation of lignin model compounds (p-hydroxybenzoic acid, vanillic acid, and syringic acid) and hardwood and softwood lignin samples was studied. It was concluded that methoxy substituents increased the reactivity toward peroxide oxidation. The succinic acid yield was higher for the model compounds with fewer methoxy groups, achieving 5.8 wt % of succinic acid for p-hydroxybenzoic acid. For Eucalyptus globulus kraft lignin (hardwood lignin with guaiacyl and syringyl units), an increased reactivity was verified, and more succinic acid (3.5 wt %) was produced in a shorter time, comparatively with Indulin AT lignin (softwood lignin, with only guaiacyl units), which produced 2.7 wt %. This evidence suggests that E. globulus kraft lignin might be a better raw material than Indulin AT for succinic acid production by peroxide oxidation.