Prefer people to persons in nearly all written contexts—using persons is dated except in select set-phrases such as persons of interest and missing persons, though the latter is restricted to small groups of people. A disappeared couple may be missing persons, but unaccounted victims of an earthquake would be missing people.
The traditional distinction, according to Bryan A. Garner, is to reserve people for general masses and persons for small, specific groups (e.g., our supreme court of nine persons judges laws for over three-hundred-million people). But this distinction may not be as certain as Garner suggests: 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.