The effect of two different interaction potentials, a two-body potential, on thermal cluster reaction rates was studied for 2-13 atom nickel clusters using the classical trajectory method. The reaction rates were computed for cluster-monomer and cluster-cluster collisions at T = 1200 K, using the bulk and dimer parametrized Lennard-Jones (LJ) potentials and were compared with the rates previously obtained for these collisional events by using a more realistic many-body tight-binding second moment approximation (TB-SMA) potential. For cluster-monomer collisions, close agreement exists between the reaction cross section results for dimer fitted LJ (LJD) potential and TB-SMA potential suggesting that the cluster-monomer collisions may be dominated by pairwise interactions. The bulk fitted LJ potential (LJB) underestimates the sticking cross section results of the other two potentials for most cluster sizes. This discrepancy however appears to be due to the relatively smaller cluster binding energies obtained for this potential as a result of which a larger cross section for dissociation is observed. For cluster-cluster collisions, for most cluster sizes, no agreement exists between the reaction cross section results for the three potentials. The discrepancy between the cross section results for the LJ potentials and the TB-SMA potential appears to lie in the difference in the scaling of cluster energy with cluster coordination for these two types of potentials (i.e., linear for LJ vs square root dependence for TB-SMA). Some characteristics of the cross section results of both LJB and LJD potentials correlate with the relative cluster stability pattern for the LJ clusters. For TB-SMA case, no such correlation exists, which however is consistent with the smooth and featureless size distributions observed experimentally for nickel and other transition metals. The cut-off used in the TB-SMA potential appears to lead to a significant underestimation of the total reaction cross section for N = 13, in the case of the cluster-cluster collisions. The results of this study indicate that the rate calculations may be sensitive to both the nature and parameterization of the simulation potential depending on the temperature range considered and cluster growth process simulated.