We present a comparison between approximated methods for the construction of mock catalogues based on the halo-bias mapping technique. To this end, we use as reference a high-resolution N-body simulation of 38403 dark matter particles on a 400 h-1 Mpc cube box from the Multidark suite. In particular, we explore parametric versus non-parametric bias mapping approaches and compare them at reproducing the halo distribution in terms of the two- and three-point statistics down to ∼ 10^8 M_{☉ } h^{-1} halo masses. Our findings demonstrate that the parametric approach remains inaccurate even including complex deterministic and stochastic components. On the contrary, the non-parametric one is indistinguishable from the reference N-body calculation in the power spectrum beyond k=1 h Mpc^{-1}, and in the bispectrum for typical configurations relevant to baryon acoustic oscillation analysis. We conclude that approaches which extract the full bias information from N-body simulations in a non-parametric fashion are ready for the analysis of the new generation of large-scale structure surveys.