Ideal thermophotovoltaic (TPV) converters approach Carnot efficiency in the limit of monochromatic radiative transfer, motivating the design of narrowband thermal emitters and absorbers. Here, we investigate whether this trend holds for converters with realistic losses by studying the effects of transmission bandwidth on the performance of far-field and near-field TPV and thermophotonic (TPX) converters. To bridge the near-field and far-field regimes, the analysis relies on an approximation that the near-field spectral energy flux is a scaled version of the far-field flux, which is validated for weakly absorbing materials using a rigorous near-field simulation. We show that the optimal bandwidth depends on the type of converter. For far-field TPVs with realistic heat losses, narrowband transport is typically detrimental to the efficiency because the converter becomes more susceptible to parasitic loss. However, narrowband transport boosts efficiencies in TPX converters and near-field TPVs as long as the excitation barrier is comparable with the thermal energy. Given the same excitation energy barrier as TPVs, TPX converters benefit from a larger available photon density of states due to the applied bias. This study suggests that near-field TPX converters with a large applied bias have the largest ratio of useful energy flux to parasitic loss. Leveraging this mechanism for actual improvement is contingent on large near-field enhancements improving photon extraction.