What is the conflict in the story "The Storyteller" by Saki?

The first conflict is between the aunt and the bachelor. The aunt gives the children a mundane, boring story. She is careful to make her story "proper." Thus, it lacks anything salacious, violent, or anything that suggests improper behavior. The bachelor counters with his own story. His story begins much like the aunt's story. It is about a girl who is quite proper. But the bachelor introduces the girl (Bertha) as "horribly good." This oxymoron draws the children in. Given the aunt's strict ideas about a "proper" story, she probably does not like the use of "horrible" and "good" in the same description. The bachelor ends the story with a violent act. The wolf eats Bertha. Note that Bertha's medals of goodness give her away. The bachelor's story (within Saki's own story) suggests that being too good is not always preferable. This is certainly the case with using a story to entertain children. If the story is all about goodness and proper behavior, children are less likely to be interested. The bachelor adds that he was able to keep the children quiet and interested, while the aunt was unable to do this. 

So, this conflict is about the best ways to instruct children and/or keep their attention. The story suggests that interesting and exciting tales and strategies are better for entertaining and educating children.