Well, I wouldn't necessarily say your are "missing" anything, but there are some reasons why using a full sub-domain might be a better plan than using a sub-directory.
1) If you need different environments for applications (PHP4 for one program, and PHP5 for another).
2) To simplify .htaccess based apache re-write rules and avoid potential conflicts.
3) To establish different email address systems (firstname.lastname@example.org and email@example.com)
4) to keep separate versions of content (dev.yourdoman.tld, old.yourdomain.tld, etc.)
I'm sure there are likely others also; these are the things that generally impact my decision to use a subdomain.