We consider approximations of scalar conservation laws obtained by adding non-local diffusive operators. In particular, we compare solutions associated to fractional Laplacian and fractional Rosenau perturbations and show that for any t > 0 the mutual L1 -distance of their profiles is lower than their common distance to the underlying inviscid entropy solution. We provide explicit examples showing that our rates are optimal in the subcritical case, in one space dimension and for convex fluxes.