As fs137 answered, a quantum computer can simulate a classical computer, and so from a purely complexity theory perspective, the classical computer is never superior to the quantum in an asymptotic sense (assuming $P\subset BQP$, currently an open question).
However, quantum computers currently operate with very low numbers of qubits (ruling out adiabatic QC like D-Wave) relative to classical computers with classical bits. Thus, we are not currently in a time where quantum computers can work at a scale where these asymptotics take over. Since quantum computers have a very large overhead to perform an operation that's comparatively simple on a classical computer, they have very large constant factors that dominate for small computations. Any single operation that a classical computer can perform, it will likely be much slower on a quantum computer.
With this in mind, classical computers dominate at small numbers of bits from a practical perspective. However, as we begin to scale the number of bits up, and we are solving a problem with a known quantum algorithm that improves upon the best known classical algorithm, we will see that a quantum computer can finish computations faster because it is executing an entirely different algorithm than the classical computer.