The classical and quantum dynamics of diatomic molecules driven by chirped laser pulses are investigated, with particular attention given to the dependence of the classical-quantum correspondence on the microscopic parameters of the systems. For this purpose, several molecules with different effective Planck's constants are employed and their respective results are compared. Based on the bucket dynamics which has been successfully applied to explain the dissociation mechanism, we propose a criterion that determines whether a particular molecule will show a good correspondence between classical and quantum calculations in a given parameter region. It is found that, when the size of the bucket is bigger than the effective Planck's constant, the classical predictions of dissociation probabilities agree well with the quantum mechanical results.