Semantics is traditionally concerned with program equivalence, in which all pairs of programs which are \emph{not} equivalent are treated the same, and simply dubbed as incomparable. In recent years, various forms of program \emph{metrics} have been introduced such that the distance between non-equivalent programs is measured as an element of an appropriate quantale. By letting the underlying quantale to \emph{vary} as the type of the compared programs become more complex, the recently introduced framework of differential logical relations allows for a new contextual form of reasoning. In this paper, we show that all this can be generalised to \emph{effectful} higher-order programs, in which not only the \emph{values}, but also the \emph{effects} computations produce can be appropriately distanced in a principled way. We show that the resulting framework is flexible, allowing various forms of effects to be handled, and that it provides compact and informative judgments about program differences.