"Persons" is NOT the plural for person, "people" is the plural for person. The only time you can use "persons" is when you are talking about the general, abstract form of people. Unless you use "persons" in this very limited context, your usage will be incorrect.
CORRECT: People today are much busier than the people of 50 years ago.
INCORRECT: Persons of today are much busier than persons of 50 years ago.
The reason that sentence two is incorrect is because there is no 'general, abstract thought' here. The sentence is about a whole group, not about any idea, thought, or imagined individual. BUT, check out the next sentence.
CORRECT: Persons with a disability should seek shelter here.
CORRECT: People with a disability should seek shelter here.
The difference between the first and second sentence is that the first is trying to express a polite, abstract idea of talking to one person but knowingly addresses a group of individuals. The second sentence, however, is not addressing an individual, but, rather, is addressing the whole group and is thus being more direct.
REMEMBER: Unless you use "persons" in the abstract form, it will be incorrect - at least in American English, which is what I, personally, teach. In other dialects of English, it may be different. It's always better to use "people" if you need to use the plural of "person".
Hope this helps! :)