You care about Turing completeness if you are trying to express something that requires it (which is something that frequently needs to be done in stored procedures). Also, SQL is not a data storage engine it is a query language.

ANSI SQL is not vendor specific but it is just a standard not an implementation. As a result you have to rely on vendors to implement the language. Many vendors deviate from the standard. This means that you cannot just write ANSI SQL and expect it to work on all databases.