It's a nice question, it will be difficult to compare their accuracy and efficiency in a single plot, because the band gap problem is mainly divided into two parts: the self-interaction and the correlations, so it depends on the material. In all cases the GW approximation is the most accurate approximation, it describes the occupied states slightly like Hartree-Fock but has the advantage of describing the unoccupied states very accurately at the expense of computational time, here is a quantitative analysis. In general, all these approximations aim at reducing the computational time without degrading the accuracy.
The self-interaction error is a wrong description of occupied states by DFT, the correction needs to include a part of the Hartree-Fock exact exchange free of a self-interaction error to build a hybrid functional (PBE0, HSE06).
Hybrid functional are useless for strongly correlated systems, the problem is not the locality of the DFT exchange but the overall approximation limited to one electron. A standard DFT cannot describe the ground state, DFT+U is the best correction and the functional used is important. Localized orbitals in this case require more derivative of the density. The SCAN+U method is often more accurate than GGA+U or LDA+U, especially for ionic solids.
I don't know the correction of the Koopmans functional, but I guess it reduces the self-interaction error and brings back the Koopmans theorem.