This paper extends the verification and validation of MCNP6’s unstructured mesh (UM) features for neutron transport capabilities by comparing code and experimental results for two different sets of experiments. The first set of experiments comprises time-of-flight spectrum measurements of spheres pulsed by 14-MeV neutrons performed by Lawrence Livermore National Laboratory in the early 1970s. The second set of experiments comprises spontaneous fission neutron attenuation measurements in relatively simple geometries with varying shield thicknesses performed by Ueki et al. in the early 1990s. First, traditional constructive solid geometry (CSG) models are analyzed to ensure agreement with experimental values and to form a basis of comparison with UM results. For the pulsed sphere experiments, a series of UM calculations is performed using first-order tetrahedral elements with various levels of mesh refinement. For the Ueki experiments, purely CSG, purely UM, and hybrid CSG/UM calculations are performed using first- and second-order tetrahedral and hexahedral elements. In the purely UM cases, two different meshing algorithms are used to specify the first-order tetrahedral mesh. The pulsed sphere calculated and experimental time-of-flight spectra agree with p-values >0.999 when compared using χ2 goodness-of-fit tests. Furthermore, the UM results show discrepancies with the experimental values comparable to the CSG cases. The Ueki neutron attenuation calculated values using track-length and point detector tallies agree with the experimental values within 1σ with a single exception that agrees well within 2σ. As such, we conclude that the results for the CSG and UM calculations agree among themselves and with the experimental quantities when considering the associated statistical uncertainties.