Performance of unsupervised compared to supervised learning on labeled data Imagine we have a labeled dataset. I always thought that a supervised algorithm would outperform an unsupervised one when applied to labelled data because it can learn from the observations. Is that true? Can a data scientist get any insight from applying an unsupervised learning algorithm on labeled data that he cannot get with a supervised one?
 A: 
Can a data scientist get any insight from applying an unsupervised
  learning algorithm on labeled data that he cannot get with a
  supervised one?

Yes, because supervised and unsupervised methods are used for different purposes. You could start with Unsupervised, supervised and semi-supervised learning thread that describes differences between those groups of methods. In unsupervised case you could be interested in finding some distinct groups in your data, e.g. by using cluster analysis. In such case algorithm looks for similarities between your cases that can help for grouping them. In supervised case you have variable or variables that you want to use to predict values of other variable or variables.
Example
With unsupervised methods you could try to look for groups of customers who have different shopping patterns, this could help you to learn more about those groups e.g. to create profiled advertising. With supervised methods you could try to find out what makes people to make purchases, what is more or less efficient, so to make predictions or to adjust to customer behavior and try to influence it. You could try to learn what generally is makes people to buy your products, but you can also ask specific questions: what makes females respond to your advertising and what makes males respond to it? Finally, there are methods that are somewhere in-between.
