  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 HII 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) 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 >~ -19.5 or M_* <~ 10^{10.4}
M_sun). 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.
