We compare Raman and infrared spectra of the nuOH/OD modes in benzoic acid crystal powders at 7 K. The extremely sharp Raman bands contrast to the broad infrared profiles and suggest adiabatic separation of hydrogen (deuterium) dynamics from the crystal lattice. There is no evidence of any proton-proton coupling term. The assignment scheme is consistent with a quasisymmetric double-minimum potential, largely temperature independent. Tunnel splitting is a major band shaping mechanism, in addition to anharmonic coupling with lattice modes. The proton/deuteron dynamics are rationalized with nonlocal pseudoparticles and extended states. We propose a symmetry-related damping mechanism to account for the broad infrared profiles, as opposed to the sharp Raman bands. We assign spectral features to distinct interconversion mechanisms based on either pseudoparticle transfer or adiabatic pairwise transfer. We establish close contacts with theoretical models based on first-principles calculations.