  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.
