In this work we have carried out a detailed classical and quantum dynamical study of a model cavity-mediated isomerization process. Our results provide insights into the recent findings of Fischer et al on the same system and confirm the viewpoint that facile energy flow from the system to the cavity mode results in the suppression of the isomerization probability. We summarize the key findings as follows. Firstly, whether coupling to the cavity results in suppression or enhancement of the isomerization is dependent on the choice of the initial state.