What might make one persons story more believable or plausible another persons

Proven arguments and confidence when speaking.

Explanation:

When a person tells a story by speaking with confidence, he expresses a sense of truthfulness and reliability. This can make the speech and the story more credible and plausible, especially when the story is made up of proven arguments and facts, which the person is able to report without difficulty and fluently.

People with difficulty in discerning the facts and arguments of a story, end up losing confidence and their speech is unreliable.