When should you prefer one type over another?
Personal preference plays a part, of course, but there are structural considerations, too.
Chapbooks are no less robust than perfect bound books, but they lend themselves to smaller texts. That's not to say that you couldn't publish a novel of 250 pages as a chapbook - you could, but a book that size looks better with a full colour cover. Chapbooks fill the space between magazines or booklets that are designed for a single reading and books which are designed to sit on a library shelf for years. That's why they are so popular with poets publishing small collections of new work: they offer an opportunity to try out the readership; to see what works and what doesn't.
If you want to publish three short stories, a chapbook would be perfect. If you have a whole collection, you would be well advised to publish them in a perfect bound paperback.
Cost is another factor, of course. It costs twice as much to produce a paperback as a chapbook.