The replacement of fossil fuel with renewable energy sources seems as though it will be crucial in the future. On the other hand, waste generation increases year by year. Thus, waste-to-energy technologies fit in with the actual trends, such as the circular economy. The crucial type of generated waste is municipal solid waste, which is in the research area. Regarding the organic fraction of municipal solid waste (OFMSW), anaerobic digestion (AD) allows the recovery of biogas and energy. Furthermore, if it is supported by source segregation, it should allow the recovery of material as fertilizer. The AD process performance (biogas yield and stability) comparison of source-segregated OFMSW (ss-OFMWS) and mechanically sorted OFMSW (ms-OFMSW) as feedstocks was performed in full-scale conditions. The daily biogas volume and methane content were measured to assess AD efficiency. To verify the process stability, the volatile fatty acid (VFA) content, pH value, acidity, alkalinity, and dry matter were determined. The obtained biogas yield per ton was slightly higher in the case of ss-OFMSW (111.1 m3/ton), compared to ms-OFMSW (105.3 m3/ton), together with a higher methane concentration: 58–60% and 51–53%, respectively, and followed by a higher electricity production capacity of almost 700 MWh for ss-OFMSW digestion. The obtained VFA concentrations, at levels around 1.1 g/kg, pH values (slightly above 8.0), acidity, and alkalinity indicate the possibilities of the digester feeding and no-risk exploitation of either as feedstock.