In view of their key role in radiation shielding and nuclear instrumentation applications, photonuclear reactions are receiving growing attention. In this work, we compare the results of the Monte Carlo codes TRIPOLI4®, DIANE, and MCNP® with respect to the Barber and George (B&G) benchmark, with the aim of assessing the accuracy of both nuclear data and particle transport codes for the simulation of photonuclear reactions. We compute the photoneutron yield resulting from the Bremsstrahlung radiation induced by a monoenergetic electron beam (10.5 to 35.5 MeV) impinging on C, Al, Cu, Pb, Ta, and U material targets. The simulation specifications closely follow those of the B&G experiment. For all codes, the reference nuclear data libraries are ENDF/B-VII.1 for neutron transport and photonuclear reactions and EPDL97/EEDL97 for photon/electron transport. Comparisons of the simulation results show an overall agreement between the codes and experimental data and in-between codes, despite some discrepancies. In order to investigate these effects, we performed a sensitivity analysis by tallying the photon production in addition to neutron production by replacing the electron source with a pure photon source (to single out the impact of electron transport) and by replacing the ENDF/B-VII.1 library with the IAEA/PD-2019. The major contribution to the observed discrepancies is found to be related to the electromagnetic shower models used for coupled electron-photon transport in Monte Carlo code