DFS vs. Union Find for computing connected components of a static graph
When the graph is dynamic, union-find can update the list of connected components in time $O(\alpha(V))$ per vertex or edge, whereas it is not clear how to run DFS progressively. So we can complement the statement you quote by


  When the edges of the graph are dynamic – changing over time – DFS is not a good choice since it cannot be applied progressively; we can compute the connected components faster by using union-find.


That said, union-find is helpful only if edges and vertices are never deleted.