Prefer people to persons in nearly all written contexts. The traditional distinction, according to Bryan A. Garner, is to reserve people for general masses and persons for small, specific groups (e.g., the U.S. supreme court of nine persons judges laws for over three-hundred-million people). But this distinction may not be as certain as Garner proposes—in the earlier 1900s, Eric Partridge already suggested that people should be preferred except in legal or formal contexts, and H.W. Fowler makes no mention of the two terms together.
It is thus safe to consider persons a dated word except in set phrases referring to small, distinctly–numerated groups of people (e.g., persons of interest and missing persons). A disappeared couple may be missing persons, but unaccounted victims of an earthquake would be missing people.