The dynamics of model membranes can be highly heterogeneous, especially in more ordered dense phases. To better understand the origins of this heterogeneity, as well as the degree to which monolayer systems mimic the dynamical properties of bilayer membranes, we use molecular simulations to contrast the dynamical behavior of a single-component dipalmitoylphosphatidylcholine (DPPC) lipid monolayer with that of a DPPC bilayer. DPPC is prevalent in both biological monolayers and bilayers, and we utilize the widely studied MARTINI model to describe the molecular interactions. As expected, our simulations confirm that the lateral structure of the monolayer and bilayer is nearly indistinguishable in both low- and high-density phases. Dynamically, the monolayer and bilayer both exhibit a drop in mobility for dense phases, but we find that there are substantial differences in the amplitude of these changes, as well as the nature of molecular displacements for these systems. Specifically, the monolayer exhibits no apparent cooperativity of the dynamics, while the bilayer shows substantial spatial and temporal heterogeneity in the dynamics. Consequently, the dynamical heterogeneity and cooperativity observed in the bilayer membrane case arises in part due to interlayer interactions. We indeed find a substantial interdigitation of the membrane leaflets which appears to impede molecular rearrangement. On the other hand, the monolayer, like the bilayer, does exhibit complex non-Brownian molecular displacements at intermediate time scales. For the monolayer system, the single particle motion can be well characterized by fractional Brownian motion, rather than being a consequence of strong correlations in the molecular motion previously observed in bilayer membranes. The significant differences in the dynamics of dense monolayers and bilayers suggest that care must be taken when making inferences about membrane dynamics on the basis of monolayer studies.