Adaptive Control of Thought-Rational (ACT-R) and the Linear Ballistic Accumulator (LBA) were compared in a model mimicry simulation of the Psychomotor Vigilance Task (PVT), a simple, reaction time (RT) task requiring sustained attention. The models use different formalisms to capture the full response profile of the PVT. The parameters were varied systematically to illustrate the ranges of the models’ predictions, to assess the models’ estimation properties, and to determine which parameters in the models correspond with each other. Both models produced skewed RT distributions typical of empirical data, including false starts and lapses. The simulation study demonstrated that both models and their parameters are recoverable. Lastly, isolated parameters in the LBA model captured the effects of varying parameters in the ACT-R model, but the reverse was not always true. These interesting correspondences across different modeling formalisms suggest the possibility of integrating ACT-R and the LBA in future work.