Bioplastics have emerged as a promising alternative to conventional plastics, marketed as environmentally friendly and sustainable materials. They provide a variety of methods for efficient waste management contributing to the goals of the circular economy. At their end-of-life stage, bioplastics can generate added value through aerobic and anaerobic biological treatments (composting or anaerobic digestion). In this study, biomethane potential (BMP) tests were carried out under mesophilic conditions on eight different catering biodegradable plastics available in the market and certified as being biodegradable under industrial composting conditions. Chemical analysis of the biodegradable plastics included elemental analysis, Fourier-transform infrared spectroscopy, and inductively coupled plasma–optical emission spectrometry. Key differences were observed in total solids (TS) and volatile solids (VS) contents between the studied biopolymer products. TS values ranged between 85.00 ± 0.26% (Product 8) and 99.16 ± 0.23% (Product 4), whereas VS content ranged between 64.57 ± 0.25 %wm (Product 6) and 99.14 ± 0.17 %wm (Product 4). Elemental analysis (elements C, H, N, S, and O) was used to estimate the theoretical methane production (ThBMP) of each product. The highest ThBMP (538.6 ± 8.7 NmL/gVS) was observed in Product 4 correlated with the highest C and H contents, while the lowest ThBMP (431.8 ± 6.1 NmL/gVS) was observed in Product 2. Significant differences were recorded between BMP values according to the chemical composition of the polymers. The average of BMP values ranged between 50.4 ± 2.1 NmL/gVS and 437.5 ± 1.0 NmL/gVS. Despite being characterized by the same composition (cellulose/cellulose derivatives and calcium carbonate), Products 2, 3, and 6 revealed significant differences in terms of TS, VS, ThBMP, and BMP. Furthermore, a significant statistical relationship (p < 0.001) was found between time (days) and BMP values of the eight products (R2 = 0.899–0.964) during the initial phase. The study confirmed that cellulose-based materials can convert efficiently under mesophilic conditions into methane, at a relatively short retention time; hence, they can be regarded as a promising material for co-digestion with feedstock in industrial anaerobic biogas plants. In contrast, biodegradation of polylactic acids (PLA) does not occur under mesophilic conditions, and hence, pre-treatment of the polymers is recommended. Moreover, PLA-containing products are highly affected by the presence of other components (e.g., polybutylene adipate terephthalate and cellulose/cellulose derivatives).