Take, for example, the hydrogen atom. Both the classical and the quantum models are based on the same Hamiltonian, describing the Coulomb potential. The classical model however misses a lot of important properties like the discrete energy spectrum. The quantum model does the job right (of course, the simple Coulomb model only works well to some limit, but that is another story).
Apparently, to obtain the correct observables like the energy spectrum one only needs to know that the right description is quantum. No new parameters which are model-specific appear (Plank's constant is universal).
Speaking more generally and more loosely, the quantum description becomes relevant at a very small scale. It seems natural to expect that a lot more details are visible at this scale. However, the input of our model, the Hamiltonian, stays basically the same. Only the general theoretical framework changes.
Probably, the question may be rephrased as follows. Why do the quantization rules exist? By the quantization rules I mean the procedures that allow to go from the classical description to the quantum in a very uniform fashion that is applicable to many systems?
Most likely my question is not too firm and contains some wrong assumptions. However, if it were not for this confusion I would not be asking!
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