What makes one way of organizing an argument superior to another?

The efficacy of an argument rests within those you are presenting it to, rather that the one you are engaged with or the methods employed in its construction. Many arguments have no chance whatever of winning the consent of the other party and are focused on persuading third parties of other things on multiple levels.

Logic is often useful, but very often invalid due to linguistic or conceptual faults and mis-interpretations. Interchanges of ideas not based on logic are persuasion, not argument. They depend upon a mutual mindset underlying the issue at hand.

Interestingly enough, choosing to avoid arguing in the first place is possible in almost every situation in everyday life. Courtrooms and other formal arenas have structure imposed as well as the organization of the opposing presentations, which entirely changes that paradigm.

The felicity of an argument depends on its content, its presentation, as well as its audience. All good arguments, however you construct it, have an edge (no matter how skillfully hidden). The point of an argument is to let someone see something as if it were new: basically, it makes someone go, Now why didn't I see that before? It's to open, without one even noticing the cut. This is an idea of argumentation going back to Socrates.

It will depend on the audience. The audience has its preferences. I for one like real life stories and facts. I do not like arguments embellished with fictional occurrences. I also prefer precision, concision and a well structured or organized exposition of the facts. What makes it superior to me is that it is closer to the truth, and real life occurrences, which I may use as reference to support my own findings.

It depends on what the purpose is.

For selfstudy: your argument should be logically and empirically sound. It should also be constructed as simple as possible. (in order that it can be easily refuted or remembered). You have to keep doubting whatever argument you created, in order to be sure it is sound.

For debate: here rethorics is also allowed (even fallacies), whatever it takes to convince an audience. Humor is a great tool. Here your goal is to make your arguments difficult to refute. You have to appear to believe your own arguments in order to convince others.

Both are necessary to construct an argument, which can stand on itself against criticism.

depends whats being argued. one system isnt always better, you gotta adapt your strategies to whats being argued