First, I beware of "A or B?" questions -- because that could be a 'false dichotomy', and a better answer might be "both", or "neither", or "something else entirely" -- or perhaps the question is unanswerable in its present form e.g. without more information.
Second, I don't see how "telling a story with a moral" is supposed to work: because either they don't recognise their own behaviour in the story (in which case it's ineffective and a waste of time); or they do recognise that the story is intended as a critique of their own behaviour, in which case how is it any different from an "accusation"?
Third, when we read the suttas we are reading stories about other people. But the dialogs in the suttas tend to be people talking to each other, they're not telling stories or talking about other people. I'm saying that "telling stories and talking about other people" doesn't seem to be the way that people talked to each other in the suttas.
Some of the teaching in the suttas takes the form of asking questions.
Perhaps "asking questions" might be one of the ways to appear less offensive -- instead of imposing your view on someone (e.g. "You are flattering this person"), you are asking for their view, like asking their advice ("Are you flattering this person?"). So perhaps a line of questioning like, "Are you flattering this person? Is that a good idea? Are you worried that might have such-and-such disadvantage?" is a way to have a conversation with the person about your concerns, while being less of an accusation, and more respectful in that it's asking them to share their view instead of imposing your own view.
And if they do answer, maybe avoid using their answer as an excuse to argue with them!
Another way to try to avoid offence is to use "I messages" i.e. talk about "I" -- for example not, "You're wrong to flatter people" (which is a "you" message), not even "Flattery is wrong" (which is still an accusation), but "I am afraid that flattery has such-and-such disadvantage" (which is an "I" message).
And if you're going to tell a story with a moral, then a story based on your own personal experience might be seen as friendlier (and perhaps more truthful) -- "sharing your own experience", for your welfare and for theirs, instead of "moralizing".
See also What is the Buddhist view in Socratic questioning?
on the subject of "asking questions" (and of "teaching by asking questions").
According to AN 4.42 there are a variety of ways to answer questions, and I expect it's done more or less skilfully. Note also AN 5.159 which says teaching should be with the thought of speaking "without exalting oneself or putting other people down", and isn't easy.
The whole topic might be linked to "conceit" -- see Māna (Wikipedia)" and How are 'conceit' and 'identity-view' not the same? -- and difficult to perform well.