Vibrational energy relaxation (VER) of solvated polyatomic molecules can occur via different pathways. In this paper, we address the question of whether treating VER classically or quantum-mechanically can lead to different predictions with regard to the preferred pathway. To this end, we consider the relaxation of the singly excited asymmetric stretch of a rigid, symmetrical, and linear triatomic molecule (A-B-A) in a monatomic liquid. In this case, VER can occur either directly to the ground state or indirectly via intramolecular vibrational relaxation (IVR) to the symmetric stretch. We have calculated the rates of these two different VER pathways via classical mechanics and the linearized semiclassical (LSC) method. When the mass of the terminal A atoms is significantly larger than that of the central B atom, we find that LSC points to intermolecular VER as the preferred pathway, whereas the classical treatment points to IVR. The origin of this trend reversal appears to be purely quantum-mechanical and can be traced back to the significantly weaker quantum enhancement of solvent-assisted IVR in comparison to that of intermolecular VER.