IMAP can be thought of as a remote file server, while POP3 can be thought of as a "store-and-forward" service. They both accomplish similar tasks.
For individual email accounts (i.e. one user) Farbyte recommends using POP3, as this method enables the user to have local copies of their emails.
For shared email accounts that are viewed by many people in your organisation / family, we recommend IMAP, as this provides centrally stored copies of any emails, thus viewable to all users.