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The measurement of neutrino oscillations and exotic physics searches are important parts of the physics program in the near future, with new state-of-the-art experiments planned within the next decade. Future and modern experiments in these fields will make use of nuclear targets. Event Generators (EGs) are software used in the analysis of neutrino oscillation experiments. EGs use to predict kinematic observables for a range of neutrino energies. These simulations may lack physics captured by more rigorous theoretical calculations. This work compares EG performance to nuclear theory calculations by comparing observables generated in the two frameworks. We provide a common set of definitions between theory and experiment and assess the physics contained in EG simulations. Neutral current quasi-elastic (NCQE) scattering events for neutrinos and anti-neutrinos on a $^{12}$C target are simulated with a specific EG, NEUT, used by the T2K experiment for its analysis. The simulated cross sections are compared to analytic calculations from nuclear theory within the factorization scheme. We compare the NEUT implementation of two different models on nuclear spectral functions: the Relativistic Fermi Gas (RFG) and the correlated basis spectral function (CBF) to analytic calculations of the same models in the factorization scheme. For both nuclear physics models, we compare the appearance of features in the distributions relevant to experimental analyses. Qualitatively, the shape of the simulated distribution is similar to the one obtained through theory calculations; however, there are some discrepancies between the theory calculations and the NEUT simulation. While the EG simulations and analytic calculations with the same model of nuclear dynamics show similar overall features, there are still differences between the two.