Elaboration of Pd-supported catalysts for catalytic combustion is, nowadays, considered as an imperative task to reduce the emissions of methane. This study provides new insight into the method of deposition, chemical state of Pd and oxygen storage capability of transition metal ions and their effects on the catalytic reactivity of supported catalysts for the combustion of methane. The catalyst with nominal composition La(Co0.8Ni0.1Fe0.1)0.85Pd0.15O3 was supported on SiO2-modified/γ-alumina using two synthetic procedures: (i) aerosol assisted chemical vapor deposition (U-AACVD) and (ii) wet impregnation (Imp). A comparative analysis shows that a higher catalytic activity is established for supported catalyst obtained by wet impregnation, where the PdO-like phase is well dispersed and the transition metal ions display a high oxygen storage capability. The reaction pathway over both catalysts proceeds most probably through Mars–van Krevelen mechanism. The supported catalysts are thermally stable when they are aged at 505 °C for 120 h in air containing 1.2 vol.% water vapor. Furthermore, the experimentally obtained data on La(Co0.8Ni0.1Fe0.1)0.85Pd0.15O3—based catalyst, supported on monolithic substrate VDM®Aluchrom Y Hf are simulated by using a two-dimensional heterogeneous model for monolithic reactor in order to predict the performance of an industrial catalytic reactor for abatement of methane emissions.