We benchmark many-body perturbation theory against density functional theory (DFT) for the band gaps of solids. We systematically compare four GW variants—G0W0 using the Godby-Needs plasmon-pole approximation (G0W0-PPA), full-frequency quasiparticle G0W0 (QPG0W0), full-frequency quasiparticle self-consistent GW (QSGW), and QSGW augmented with vertex corrections in W (QS \(G\hat{W}\) )—against the currently best-performing and popular density functionals mBJ and HSE06. Our results show that G0W0-PPA calculations offer only a marginal accuracy gain over the best DFT methods, however, at a higher cost. Replacing the PPA with a full-frequency integration of the dielectric screening improves the predictions dramatically, almost matching the accuracy of the QS \(G\hat{W}\) . The QSGW removes starting-point bias, but systematically overestimates experimental gaps by about 15%. Adding vertex corrections to the screened Coulomb interaction, i.e., performing a QS \(G\hat{W}\) calculation, eliminates the overestimation, producing band gaps that are so accurate that they even reliably flag questionable experimental measurements.
