  We present a comparison of various approximations to self-consistency in the
GW method, including the one-shot G0W0 method, different quasiparticle
self-consistency schemes, and the fully self-consistent GW (scGW) approach. To
ensure an unbiased and equitable comparison, we have implemented all the
schemes with the same underlying Matsubara formalism, while employing Gaussian
orbitals to describe the system. Aiming to assess and compare different GW
schemes, we analyze band gaps in semiconductors and insulators, as well as
ionization potentials in molecules. Our findings reveal that for solids, the
different self-consistency schemes perform very similarly. However, for
molecules, full self-consistency outperforms all other approximations, i.e.,
the one-shot and quasiparticle self-consistency GW schemes. Our work highlights
the importance of implementation details when comparing different GW methods.
By employing state-of-the-art fully self-consistent, finite temperature GW
calculations, we have successfully addressed discrepancies in the existing
literature regarding its performance. Our results also indicate that when
stringent thresholds are imposed, the scGW method consistently yields accurate
results.
