In the late 1800's, people debated the impact of corporations, calling their leaders either "robber barons" or "Captains of industry". Are such debates still relevant today?

They are. That is because due to things like the globalization, the companies get richer and the people get poorer. The division between the rich and the poor has reached unprecedented heights and that's why people often protest against big companies and big banks. Such was the occupy wall street movement.