We present here the second part of a project that aims at solving the controversy on the issue of the bar effect on the radial distribution of metals in the gas-phase of spiral galaxies . In Paper I we presented a compilation of more than 2800 H ii regions belonging to 51 nearby galaxies for which we derived chemical abundances and radial abundance profiles from a homogeneous methodology . In this paper we analyse the derived gas-phase radial abundance profiles of 12+ \log ( O/H ) and \log ( N/O ) , for barred and unbarred galaxies separately , and find that the differences in slope between barred and unbarred galaxies depend on galaxy luminosity . This is due to a different dependence of the abundance gradients ( in dex kpc ^ { -1 } ) on luminosity for the two types of galaxies : In the galaxy sample that we consider the gradients appear to be considerably shallower for strongly barred galaxies in the whole luminosity range , while profile slopes for unbarred galaxies become steeper with decreasing luminosity . Therefore , we only detect differences in slope for the lower luminosity ( lower mass ) galaxies ( M _ { B } \gtrsim - 19.5 or M _ { * } \lesssim 10 ^ { 10.4 } M _ { \odot } ) . We discuss the results in terms of the disc evolution and radial mixing induced by bars and spiral arms . Our results reconcile previous discrepant findings that were biased by the luminosity ( mass ) distribution of the sample galaxies and possibly by the abundance diagnostics employed .