Background: Complete fusion cross section measurements involving weakly bound projectiles show suppression at above-barrier energies compared to coupled-channels (CC) calculations, but no definite conclusion could be drawn for sub-barrier energies. Different CC models often lead to contrasting results.Purpose: We aim to investigate the differences in the fusion cross sections predicted by commonly used CC calculations, using codes such as fresco and ccfull, when compared to experimental data.Methods: The fusion cross sections are normalized to a dimensionless form by isolating the effect of only dynamic channel couplings calculated by both fresco and ccfull, by the method of fusion functions, and compared to a universal fusion function. This acts as a probe for obtaining the model dependence of fusion.Results: A difference is observed between the predictions of fresco and ccfull for all the reactions involving $^{6,7}\mathrm{Li}$ as projectiles, and it is noticeably more for systems involving $^{7}\mathrm{Li}$.Conclusions: With the theoretical foundations of the two CC models being different, their calculation of fusion is different even for the same system. The conclusion about the enhancement or suppression of fusion cross sections is model dependent.