In this work we perform a comparison of atomic diffusion multi-frequency models for h.c.p. lattices. Specifically, in diluted h.c.p. αZr-Nb alloy, we calculate, the tracer self- and impurity diffusion coefficients, with Ghate's eight frequencies model and with the 13 frequencies model recently developed by Allnatt et al. For the latter we investigate the tight-binding limit and the 5-frequency limit of the model. Our exhaustive calculations have been performed using, for both models, classical molecular static techniques (MS), as well as, quantum ab-initio calculations within both LDA and GGA approximations. Our ab-initio calculations show that a, so called, 5-frequency model, without pairs dissociation nor anisotropy in the jump frequencies, that only needs three frequencies, is sufficient to obtain solvent and solute anisotropic diffusion coefficients that are in agreement with experimental data.