Is there any task where classical computers outperform quantum computers?
If you're asking whether a quantum computer can compute any function that a classical computer can compute without using many more elementary computational steps, then the answer is yes: a quantum computer can perform any reversible classical computation, and if you keep the input around, any classical computation can be made reversible at a cost of multiplying the number of steps by a small constant factor.

If you're asking whether a quantum computer can compute any function that a classical computer can without using many more resources, the answer is much less clear. The construction that lets you make a $T$-step computation reversible using $O(T)$ steps also takes $O(T)$ space (i.e., memory cells). You can achieve a smaller blow-up in space at the cost of a superlinear number of steps. See Time/Space Trade-Offs for Reversible Computation by Charles H. Bennett. 

For an actual physical quantum computer, it's very likely that you might also be able to make it faithfully simulate a classical computer by letting it lose coherence, but in this case it's no longer really working as a quantum computer, and if you try to use a quantum computer that is operating this way as a subroutine in a quantum computation, it might not work properly.