The classical version is deterministic, but "deterministic" does not necessarily mean "calculable". There are plenty of deterministic problems that are not calculable (at least not in any reasonable time frame, where "reasonable" means "not of a much greater order of magnitude than the age of the universe") because they are so sensitive to precise conditions that miniscule differences quickly become unmanageably huge. And since we can never measure a system's state to exact precision, nor can we calculate things to exact precision, our model of a system is always imprecise, and for many systems, "imprecise" means "not calculable" even though the underlying laws are deterministic.
The quantum version is not even deterministic when measurements are involved.