Basically SDO is Oracle SOA's attempt at an ORM and therefore you can simple look for information on ORM compared to JDBC. The DBAdaper is slight different from plain JDBC in it has extra features around polling and stored procedure integration.
DBAdapter for -> Simple SQL, Stored procedures, basic read write, delete and update and polling SDO -> Highly reuseable code and everything that doesn't suit DBAdapter.
Here is a thread to look at http://forum.spring.io/forum/spring-projects/data/14117-jdbc-or-orm-framework-what-are-the-pros-and-cons