We study the absorption and emission electronic spectra in an aqueous solution of N-methyl-6-oxyquinolinium betaine (MQ), an interesting dye characterized by a large, change of polarity and H-bond between the ground (S-0) and the excited (S-1) states. To that,end we compare alternative approaches based either oft explicit :solvent models and density functional theory (DFT)/molecular-mechanics,(MM) calculations or on DFT calculations on clusters models embedded in a polarizable continuum (PCM). In the first approach (Cl-MD), the spectrum. is computed according to the classical Franck-Condon principle, from the dispersion of the time-dependent (TD)-DFT vertical transitions at selected snapshots of molecular dynamics (MD) on the initial state. In the cluster model (Q(st)) the Spectrum is simulated by computing The quantum vibronic structure, estimating the inhomogeneous broadening from state-specific TD-DFT/PCM solvent reorganization energies. While both approaches provide absorption and emission spectral Shapes in nice agreement with experiment, the Strokes Shift is perfectly reproduced by Q(st) calculations if S-0, and S-1 clusters are selected on the grounds of the MD trajectory. Furthermore, Q(st) spectra. better fit the experimental line shape, mostly in absorption. Comparison of the predictions of the two approaches is very instructive: the positions of Q(st) and Cl-MD spectra ate shifted due to the different solvent models and the Cl-MD spectra are narrower than the Q(st) ones, because MD underestimates the width of the vibrational density of states of the high-frequency modes coupled to the electronic transition. On the other hand, both Q(st), and Cl-MD approaches highlight that the solvent has multiple and potentially opposite effects on the spectral width, so that the broadening due to solute solvent vibrations and electrostatic interaction with bulk solvent is (partially) counterbalanced by a narrowing of the contribution due to the solute vibrational modes. Q(st) analysis evidences a pure quantum broadening effect of the spectra in water due to vibronic progressions along the solute/solvent H-bonds.