A use case description is a textual model while an activity diagram is a graphical model. These two things differ in that a textual model is a text representation of requirement descriptions that are difficult to explain in other ways while a graphical models are kind of the opposite. Graphical models are things easier to describe in visual models things that might be difficult to follow when described textually. Being a graphical model, activity diagrams can be expressed by using the Unified Modeling Language (UML) which is a standard graphical model set.
Good use of a use case description would be one that is written to accompany a use case diagram. The diagram would be similar to the activity diagram being that it would be a graphical representation and the use case description would provide the extra details not shown. This way the description can be referred to for more information to further explain the diagram.
An activity diagram is best used when showing a workflow or process. An example would be an integration system that receives a notification, translates the data from it, then directs the information to the appropriate system depending on the data it contains. The workflow can be shown graphically as the steps are clear enough to diagram while not needing too much description.