  For the paradigmatic case of H2-dissociation we compare state-of-the-art
many-body perturbation theory (MBPT) in the GW approximation and
density-functional theory (DFT) in the exact-exchange plus random-phase
approximation for the correlation energy (EX+cRPA). For an unbiased comparison
and to prevent spurious starting point effects both approaches are iterated to
full self-consistency (i.e. sc-RPA and sc-GW). The exchange-correlation
diagrams in both approaches are topologically identical, but in sc-RPA they are
evaluated with non-interacting and in sc-GW with interacting Green functions.
This has a profound consequence for the dissociation region, where sc-RPA is
superior to sc-GW. We argue that for a given diagrammatic expansion, the DFT
framework outperforms the many-body framework when it comes to bond-breaking.
We attribute this to the difference in the correlation energy rather than the
treatment of the kinetic energy.
