The potential efficacy of boron neutron capture therapy (BNCT) for malignant glioma is a significant function of epithermal-neutron beam biophysical characteristics as well as boron compound biodistribution characteristics. Monte Carlo analyses were performed to evaluate the relative significance of these factors on theoretical tumor control using a standard model. The existing, well-characterized epithermal-neutron sources at the Brookhaven Medical Research Reactor (BMRR), the Petten High Flux Reactor (HFR), and the Finnish Research Reactor (FiR-1) were compared. Results for a realistic accelerator design by the E. O. Lawrence Berkeley National Laboratory (LBL) are also compared. Also the characteristics of the compound p-Boronophenylaline Fructose (BPA-F) and a hypothetical next-generation compound were used in a comparison of the BMRR and a hypothetical improved reactor. All components of dose induced by an external epithermal-neutron beam fall off quite rapidly with depth in tissue. Delivery of dose to greater depths is limited by the healthy-tissue tolerance and a reduction in the hydrogen-recoil and incident gamma dose allow for longer irradiation and greater dose at a depth. Dose at depth can also be increased with a beam that has higher neutron energy (without too high a recoil dose) and a more forward peaked angular distribution. Of the existing facilities, the FiR-1 beam has the better quality (lower hydrogen-recoil and incident gamma dose) and a penetrating neutron spectrum and was found to deliver a higher value of Tumor Control Probability (TCP) than other existing beams at shallow depth. The greater forwardness and penetration of the HFR the FiR-1 at greater depths. The hypothetical reactor and accelerator beams outperform at both shallow and greater depths. In all cases, the hypothetical compound provides a significant improvement in efficacy but it is shown that the full benefit of improved compound is not realized until the neutron beam is fully optimized.