Chapbooks are A5, untrimmed. They have a card cover, front and back, and a plain white paper or kraft (brown) paper dust jacket printed in one colour. The spine of the book is glued.
They are not as finished as the perfect bound books, but they have a certain 'homespun' appeal.
Perfect bound books have full colour covers. The spines are glued and stitched and are very robust.
The books are trimmed to a uniform size: 14cm x 20cm.
Personal preference plays a part, of course, but there are structural considerations, too.
Chapbooks are less robust than perfect bound books and 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 really needs a stronger binding. 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.