The dreaded Elements of Style have this to say on this matter:
The word people is not to be used with words of number, in place of persons. If of "six people" five went away, how many "people" would be left?
So at least in formal or technical discourse you might want to prefer "persons".
I have also observed that "persons" is generally and widely used in official documents, highway signs, etc. in Britain, Canada, and the U.S.
In informal contexts, however, "people" is probably preferable, especially as it will allow you to steer clear of the, er, people from all walks of life who will try to tell you that "persons" is not a valid word at all.
But as both your question and Strunk point out, you should avoid mixing them too much, because there is no exact correspondence between "person"/"persons" and "people"/"peoples".