Captains of industry (or robber barons, depending on your point of view) like the ones you mention had something of a paradoxical view of competition. They thought that competition was a good thing, but they wanted to use competition to create a situation where there was no longer any competition.
People like these men believed in ruthless competition between businesses. They were eager to find ways to cut their costs so that they could put out a cheaper product and make more money. They were willing to do anything that was necessary to defeat their competitors. In that sense, they were in favor of competition.
In another sense, however, they did not like it. These men wanted to compete, but only until they destroyed all of their competitors. Their actual goal was to have no competition at all. As the first paragraph in the link below says, the “business leaders strove to eliminate competition.” They wanted to get to a point where they had monopoly power. If they could achieve this, they would no longer have to worry about the volatility that competition could create.
We can say, then, that these men liked competition, but they only wanted to compete until they had driven all their competitors out of business so that they could enjoy stability and guaranteed profits.