[EM] Where the best Condorcet methods (Schulze, Ranked Pairs, River etc.) differ (Toby Pereira)
If the Smith set is a cycle of three, then the methods you mention give the same result as long as the defeat strength is measured the same way. (You knew that)
Not all of these satisfy Independence from Pareto Dominated Alternatives. I doubt that would make a difference in any known public election from the past, but all else being equal, it is a difference that could make a difference.
Simplicity of explanation and implementation, along with heuristic appeal, and other selling points may be more important than any other distinction among the methods you mention.
For me the easiest to sell formulation of Schulze is in the form of "beat-path." But that is probably just the mathematician in me appreciating an elegant way of creating a transitive relation with minimal violence to the intransitive relation on which it is based.