Nondestructive assay (NDA) of uranium samples is typically performed using either active neutron multiplicity counting or passive gamma-ray spectroscopy. For large quantities (around 10 kg) of pure, highly enriched uranium (HEU) such as HEU oxide, active well coincidence counters (AWCCs) are widely used to detect time-correlated neutrons from neutron-induced fission with 3He tubes embedded in a polyethylene moderator. The active source used to induce the fissions is typically americium-lithium (AmLi). The purported advantage of this method over gamma-ray spectroscopic analysis is the greater penetrability of neutrons in the measured samples; however, the degree of this advantage has not been yet quantified in detail. The objective of this work is to perform Monte Carlo simulations of neutron multiplicity and gamma-ray spectroscopic analysis for the determination of the fissile mass of HEU-oxide samples. A range of such samples has been previously measured using both an AWCC and a high-purity germanium (HPGe) detector. Here, the two techniques are directly compared in their ability to detect a range of diverted uranium-oxide masses.