Progressive supranuclear palsy and Parkinson's disease have distinct underlying neuropathology, but both diseases affect cognitive function in addition to causing a movement disorder. They impair response inhibition and may lead to impulsivity, which can occur even in the presence of profound akinesia and rigidity. The current study examined the mechanisms of cognitive impairments underlying disinhibition, using horizontal saccadic latencies that obviate the impact of limb slowness on executing response decisions. Nineteen patients with clinically diagnosed progressive supranuclear palsy (Richardson's syndrome), 24 patients with clinically diagnosed Parkinson's disease and 26 healthy control subjects completed a saccadic Go/No-Go task with a head-mounted infrared saccadometer. Participants were cued on each trial to make a pro-saccade to a horizontal target or withhold their responses. Both patient groups had impaired behavioural performance, with more commission errors than controls. Mean saccadic latencies were similar between all three groups. We analysed behavioural responses as a binary decision between Go and No-Go choices. By using Bayesian parameter estimation, we fitted a hierarchical drift-diffusion model to individual participants' single trial data. The model decomposes saccadic latencies into parameters for the decision process: decision boundary, drift rate of accumulation, decision bias, and non-decision time. In a leave-one-out three-way classification analysis, the model parameters provided better discrimination between patients and controls than raw behavioural measures. Furthermore, the model revealed disease-specific deficits in the Go/No-Go decision process. Both patient groups had slower drift rate of accumulation, and shorter non-decision time than controls. But patients with progressive supranuclear palsy were strongly biased towards a pro-saccade decision boundary compared to Parkinson's patients and controls. This indicates a prepotency of responding in combination with a reduction in further accumulation of evidence, which provides a parsimonious explanation for the apparently paradoxical combination of disinhibition and severe akinesia. The combination of the well-tolerated oculomotor paradigm and the sensitivity of the model-based analysis provides a valuable approach for interrogating decision-making processes in neurodegenerative disorders. The mechanistic differences underlying participants' poor performance were not observable from classical analysis of behavioural data, but were clearly revealed by modelling. These differences provide a rational basis on which to develop and assess new therapeutic strategies for cognition and behaviour in these disorders.