The J/ψ dissociation by π and ρ mesons is examined in meson exchange model and compared to the quark interchange model. We found that the main difference between the predictions of the two models could be resolved by the form factors and the contact interactions in meson exchange model calculations. By adopting covariant form factors and adjusting the four-point couplings, we found that the meson exchange model could give similar predictions with the quark interchange models not only for the magnitudes but also for the energy dependence of the low-energy dissociation cross sections of the J/ψ by π and ρ mesons. Our finding suggests a way to understand one of the discrepancies among the existing model predictions on the J/ψ dissociation cross sections by light hadrons.