  Ultra-low-background experiments address some of the most important open
questions in particle physics, cosmology and astrophysics: the nature of dark
matter, whether the neutrino is its own antiparticle, and does the proton
decay. These rare event searches require well-understood and minimized
backgrounds. Simulations are used to understand backgrounds caused by naturally
occurring radioactivity in the rock and in every piece of shielding and
detector material used in these experiments. Most important are processes like
spontaneous fission and ({\alpha},n) reactions in material close to the
detectors that can produce neutrons. A comparison study between two dedicated
software packages is detailed. The cross section libraries, neutron yields, and
spectra from the Mei-Zhang-Hime and the SOURCES-4A codes are presented. The
resultant yields and spectra are used as inputs to direct dark matter detector
toy models in GEANT4, to study the impact of their differences on background
estimates and fits. Although differences in neutron yield calculations up to
50% were seen, there was no systematic difference between the Mei-Hime-Zhang
and SOURCES-4A results. Neutron propagation simulations smooth differences in
spectral shape and yield, and both tools were found to meet the broad
requirements of the low-background community.
