[en] We show that in SU(2) Yang-Mills theories a simple relation exists between lattice gluon propagators in the Coulomb and Landau gauges and discuss the physical implications of such result. In particular, the realization of the Gribov-Zwanziger confinement mechanism in Coulomb gauge, linked to dual superconductivity, would imply that the standard BRST charge must be ill defined nonperturbatively. As a consequence, the Kugo-Ojima confinement criterion, which relies on BRST charge conservation beyond perturbation theory, would not be fulfilled.