This is a question I’ve pondered before (see here). Today I stumbled upon the Columbia Law Review’s take on the question:
Articles tend to be research pieces analyzing a problem and suggesting a solution. Such analysis usually articulates some background information to inform the reader, before turning to a novel argument. Along these lines, published articles regularly follow a traditional roadmap of introduction, background, analysis/argument, and conclusion, and provide a comprehensive treatment of a particular area of law. Articles tend to be formal in both the author’s tone and in the obligation to ground information and analysis in comprehensive substantive support via consistent citation.
The primary purpose of essays is not to conduct new legal research but to advance an idea, summarize a development, or initiate or engage in discussion. The topics, approaches, and insights are more diverse, and the author is freer to inject personality or voice into the piece.