A well-established notion in cognitive neuroscience proposes that multiple brain systems contribute to choice behaviour. These include: (1) a model-free system that uses values cached from the outcome history of alternative actions, and (2) a model-based system that considers action outcomes and the transition structure of the environment. The widespread use of this distinction, across a range of applications, renders it important to index their distinct influences with high reliability. Here we consider the two-stage task, widely considered as a gold standard measure for the contribution of model-based and model-free systems to human choice. We tested the internal/temporal stability of measures from this task, including those estimated via an established computational model, as well as an extended model using drift-diffusion. Drift-diffusion modeling suggested that both choice in the first stage, and RTs in the second stage, are directly affected by a model-based/free trade-off parameter. Both parameter recovery and the stability of model-based estimates were poor but improved substantially when both choice and RT were used (compared to choice only), and when more trials (than conventionally used in research practice) were included in our analysis. The findings have implications for interpretation of past and future studies based on the use of the two-stage task, as well as for characterising the contribution of model-based processes to choice behaviour.