The solid-liquid equilibria phase diagrams of eight eutectic systems formed by choline chloride and fatty acids, or fatty alcohols, were measured to characterize the nonideality of the liquid phase of these systems, commonly reported in the literature as examples of type III deep eutectic solvents (DESs), and to evaluate the best modeling approaches to their description. Most of these systems are shown to present only slight deviations from ideal behavior, resulting from a fine balance of the hydrogen bonding between the hydroxyl/carboxylic groups with the chloride anion and the interactions present in the pure compounds. The phase diagrams measured were modeled with an associative equation of state (EoS) and a g(E) model. As an EoS, the perturbed-chain statistical associating fluid theory (PC-SAFT) was used, and this model was able to accurately describe the experimental data and to provide reliable estimates of the eutectic points using just a single binary temperature-dependent interaction parameter that often correlates with the acid/alcohol chain length. The performance of PC-SAFT was further compared with the g(E) model, a non-random two-liquid model (NRTL), and was found to provide a better description of the experimental data, especially for the more nonideal systems. Ultimately, the data gathered, and the molecular modeling, allowed the discussion of the behavior of fatty acids or fatty alcohols as hydrogen bond donors in choline chloride-based DESs.