I read this example somewhere last year. I don't exactly remember from where. Anyway, it goes like this.
Let us consider a family tree of a tree.

As you can see, the upper levels of the tree consists of the ancestors and the next level consists of their descendents and so on.
When to apply DFS?
If you are searching for someone who is one of the younger members of the family, that the probability of that person to be found is at the bottom of the tree. If you apply DFS, you reach the depth faster. BFS will take longer time to reach the last level.
When to apply BFS?
If you are searching for a member who died long ago or is an elder member of the family, BFS will give you good result because that person would be closer to the root of the tree.
So the answer depends on the type of problem you are about to solve.