Different degradable plastics have been promoted as a solution for the accumulation of waste in landfills and the natural environment; in Mexico, the most popular options are oxo-degradable, which degrade in a sequential abiotic–biotic process, and compostable plastics. In this research, high-density polyethylene, oxo-degradable high-density polyethylene, and certified compostable plastic were exposed to simulated landfill conditions in an 854-day-long experiment to assess their degradation. High-density polyethylene showed limited degradation, due mainly to surface erosion, evidenced by a 13% decrease in elongation at break. The pro-oxidant additive in the oxo-degradable plastic increased this loss of mechanical properties to 27%. However, both plastic films kept their physical integrity and high molecular weight by the end of the experiment, evidencing degradation but no biodegradation. While the compostable film fragmented, had a lower molecular weight at the end of the experiment, and decreased the presence of C=O bonds, this degradation took place remarkably slower than expected from a composting process. Results show that oxo-degradable and compostable plastics will not biodegrade readily in landfills. This fact should be known and understood for decision-makers to match the characteristics of the materials to the features of the waste management systems.