The catalytic activity of Cu-zeolites of different topologies: BEA, MFI, MOR, FER, and CHA, prepared by impregnation or by solid-state ion exchange, were evaluated for NO2 and N2O formation during NH3-SCR reaction with or without H2O. All catalysts obtained by solid-state ion exchange were active in wider temperature windows and exhibited higher selectivity to N2, compared to those obtained by impregnation. Regardless of the method of copper introduction, the zeolites with 3D channels (BEA, MFI, CHA) were more active than those with the 2D channel frameworks (MOR and FER). The multimodal formation of NO2 and N2O results from several identified parallel-consecutive pathways, controlled primarily by copper speciation and the reaction temperature. Decomposition of NH4NO3 occurs via thermal dissociation, dehydration, and comproportionation with NO routes. The topology of the zeolites has less influence on the extent of decomposition of NH4NO3 into N2O vs. NO2 (the N2O/NO2 ratio of 3.2–3.5 was found for all zeolites), exerting a more distinct impact on the decomposition onset. For zeolites with the 3D channels, it starts at lower temperatures, and the N2O and NO2 pathways are more separated with the increasing temperature, compared to the 2D channel zeolites. The NH4NO3 dissociation pathway is essentially controlled by Brønsted acidity of the zeolites.