No essay has a reason to exist without making a significant point. A persuasive essay makes its point through a stated thesis, and then it leads the reader through a series of logical points, finally establishing the truth of the thesis.
The narrative essay, on the other hand, more often makes its point by implication. The writer tells a fact-based story about real events and people, finally leaving the reader with an impression that suggests an implied thesis, often of a moral nature. In both cases, the writer establishes a clear point of view about the topic.
Like all essays, the writer must provide substantive support for the point that the writer wants to make. While persuasive essays offer data, statistics and other evidence to support the main point, narrative essays argue more subtly, with anecdotes and carefully selected details, all of which steer the reader toward sharing the author's view.
Both persuasive and narrative essays are expository; that is, they explain expansively, or expose causes and outcomes, problems and solutions and so forth.
Persuasive essays explain by way of fact and reason. Narrative essays explain through an exploration of human relationships and sensory impressions, as well as with facts. Narrative essays can appeal to emotion, however, by highlighting selective material and manipulating sensory impressions. This would be a serious logical flaw in a scholarly argument.
The fundamental elements of good writing are also the same in both subgenres. If a writer neglects focus, organization, significance, development or logic, the entire essay is adversely affected in either a persuasive or narrative essay. The same is true of what composition specialists call lower-order concerns, such as grammar, mechanics and spelling. If either kind of essay is peppered with lower-order errors, it fails.