What is the advantage of using Dunn index over other metrics for evaluating clustering algorithm?
They will often give the same preferences.

Do not forget that these are largely heuristics. They won't have much advantages over one another. That is why there are so many.

As a guideline, look at the definitions. Choose that index, whose equation is most relevant for your problem. (Yes, you do need to understand what they do. Clustering is hard, it is easy to get meaningless results by just looking at the code and scores and forgetting the underlying math.)