Within the framework of evidence accumulation there exist a range of models of decision making. The most popular models use relatively simple assumptions about underlying psychological mechanisms, like in the diffusion model. Other models start from plausible neural mechanisms, such as the Ising Decision Maker (IDM), which builds from the assumption that two pools of neurons with self-excitation and mutual inhibition receive perceptual input from external excitatory fields. Here, we explore the consequences of simplifying the decision process. To do this, we simulate data from the IDM and fit it with the diffusion model, looking at the relationship between the three parameters whose meaning is the same in both models: stimulus distinctness (drift rate) , detection box size (boundary separation), and non-decision time. We also explore the ways that the diffusion model, assuming a stable evidence stream, reflects the dynamic nature of the IDM.