Aerosol effects on clouds and radiation are a large source of uncertainty in our understanding of human impacts on the climate system. Uncertainty in aerosol effects results from uncertainty in parameter values, known as parametric uncertainty, and from uncertainty from the model’s structure, known as structural uncertainty. While previous studies have assessed the impact of parametric uncertainty on modeled forcing, structural errors from the numerical representation of particle distributions and their dynamics have not been well quantified. Here we present a framework for quantifying error in aerosol size distributions and cloud condensation nuclei activity, which we apply to the widely used 4-mode version of the Modal Aerosol Module (MAM4). Box model predictions from the MAM4 are evaluated against the Particle Monte Carlo Model for Simulating Aerosol Interactions and Chemistry (PartMC-MOSAIC), a benchmark model that tracks the evolution of individual particles. We show that size distributions simulated by MAM4 diverge from those simulated by PartMC-MOSAIC after only a few hours of aging by condensation and coagulation in polluted conditions, which leads to large errors in modeled cloud condensation nuclei concentrations. We find that differences between MAM4 and PartMC-MOSAIC are largest under polluted conditions, where the size distribution evolves rapidly though aging. These findings indicate that structural error in modeled aerosol properties is a key factor contributing to uncertainty in aerosol forcing.