This paper deals with the study of the equivalence between stationary distributions in conservative systems and in corresponding dissipative systems. This phenomenon allows transferring results between these two limiting cases. In particular, the momentum distributions in micro-canonical and grand-canonical ensembles of Gross-Pitaevskii equations at equipartition are the same as in a purely dissipative complex Ginzburg-Landau equation. The equivalence of temporal power spectra is shown only numerically and a clear dominance of phase fluctuations in the long wavelength limit is predicted. These results are supported by several numerical results in conservative cases.