Strictly speaking those aren't mutually exclusive. LDAP is a protocol for accessing directory services; any LDAP implementation is likely to use a database underneath as well.
LDAP generally comes with a number of functionalities that you'd have to build yourself if you used a DB directly; that may be a factor. But of course you lose flexibility with LDAP, which may or may not make a difference.
The big advantage LDAP has is that it is a standard and many third-party applications/app servers have LDAP connectors built in. This means you don't have to write the same authentication/authorization code over and over, users don't have to register and maintain accounts on dozens of different systems, administrators don't have to reset passwords or maintain accounts and so on.