A study of magnetic-field tuned superconductor-insulator transitions in amorphous $Nb_{0.15}Si_{0.85}$ thin films shows that quantum superconductor-insulator transitions are characterized by an unambiguous signature -- a kink in the temperature profile of the critical magnetic field. Using this criterion, we show that the nature of the magnetic-field tuned superconductor-insulator transition depends on the orientation of the field with respect to the film. For perpendicular magnetic field, the transition is controlled by quantum fluctuations with indications for the existence of a Bose insulator; while for parallel magnetic field, the transition is classical, driven by the breaking of Cooper pairs at the temperature dependent critical field $H_{c2}$.