By combining path-integrals molecular dynamics simulations with the accurate MB-pol potential energy surface, we investigate the role of alternative potential models on isotopic fractionation ratios between H and D atoms at dangling positions in water clusters at low temperatures. Our results show clear stabilizations of the lighter isotope at dangling sites, characterized by free energy differences ΔG that become comparable to or larger than k_BT for temperatures below ∼75 K. The comparison between these results to those previously reported using the empirical q-TIP4P/F water model [P.E. Videla et al., J. Phys. Chem. Lett. 5, 2375 (2014)] reveals that the latter Hamiltonian overestimates the H stabilization by ∼25%. Moreover, predictions from the MB-pol model are in much better agreement with measured results reported for similar isotope equilibria at ice surfaces. The dissection of the quantum kinetic energies into orthogonal directions shows that the dominant differences between the two models are to be found in the anharmonic characteristics of the potential energy surfaces along OH bond directions involved in hydrogen bonds.