Choose Oracle DBA unless you are very very

interested in software engineering and you are a very good developer.

A good DBA requires a comprehensive range of knowledge and skills. Once you get it in a few years, it is very easier than developers to locate a job, especially in harsh economy.

The simple fact is that there are many good developers, but not many good DBAs. So you will stand out easily if you have good database skills. (To be clear, good database skills means much more than writing SQL queries. It means, for example, you know how MVCC is implemented in Oracle, and consistent read is implemented, etc.)

You are fortunate that the company would have patience to train you to be Oracle DBA. Think about it.