In this study, computational models have become increasingly used as part of modeling, predicting, and understanding how infectious diseases spread within large populations. These models can be broadly classified into differential equation-based models (EBM) and agent-based models (ABM). Both types of models are central in aiding public health officials design intervention strategies in case of large epidemic outbreaks. We examine these models in the context of illuminating their hidden assumptions and the impact these may have on the model outcomes. Very few ABM/EBMs are evaluated for their suitability to address a particular public health concern, and drawing relevant conclusions about their suitability requires reliable and relevant information regarding the different modeling strategies and associated assumptions. Hence, there is a need to determine how the different modeling strategies, choices of various parameters, and the resolution of information for EBMs and ABMs affect outcomes, including predictions of disease spread. In this study, we present a quantitative analysis of how the selection of model types (i.e., EBM vs. ABM), the underlying assumptions that are enforced by model types to model the disease propagation process, and the choice of time advance (continuous vs. discrete) affect the overall outcomes of modeling disease spread. Our study reveals that the magnitude and velocity of the simulated epidemic depends critically on the selection of modeling principles, various assumptions of disease process, and the choice of time advance.