I’d place argumentation on a 2 axis scale of effectiveness tangential to efficiency.
Socratic method can be placed on there. Byzantine Rhetoric (they saw rhetoric as above and including all forms of argumentation) can be on there. Modern rational argument style (complete with rules and a list of fallacies, very commonly used online) can go on there.
I don’t know what one would use to determine where each fit on the graph, but that’s the graph I would use.