A responsive layout is in theory always better than an adaptive layout, but in some cases an adaptive layout is a more pragmatic solution. An adaptive layout will give you more control over the design because you only have a handful of states to consider. In a responsive layout you easily have hundreds of states — sure, most of them with very minor differences, but they are different nonetheless — which makes it harder to know exactly how your design will look.
An adaptive layout has its merits because it can be a more pragmatic solution that is cheaper to implement and easier to test. An adaptive layout can be considered the cheaper sibling of a responsive layout and can thus be appealing if resources are tight. This is especially true when dealing with an existing website, where a complete rewrite is not always feasible. In such cases, an adaptive layout can be a good (and more manageable) start. One argument often brought up in favor of an adaptive layout when compared to a responsive layout is that of typography — in particular better control over line lengths and avoiding orphaned header text.