These men and others like them were both “captains of industry” and “robber barons.” There is no way to say that they were all one or all the other.
These men were clearly captains of industry whose actions helped to create the powerful and modern US economy. These men had the vision and the determination to completely change the way that the American economy ran. In doing so, they created a more industrialized and modern economy that has benefited us all in the long run. In addition, many of these men became great philanthropists. As an example of this, Rockefeller’s donations created the University of Chicago and Carnegie’s built libraries all over the country.
But the ways in which these men made their money were not kind and gentle. Even today, business is a cut-throat world in ways and it was much worse back in the Gilded Age. These men were willing to take any advantage (including corrupt ones) to drive competitors out of business. They were willing to use violence against union members. They became hugely wealthy while so many were extremely poor.
Thus, it is really not possible to characterize them only as robber barons or only as captains of industry. They unquestionably had aspects of both.