To answer your question the DRS stage should be faster then the ODBC stage as it uses native database connectivity. You will need to install and configure the required database clients on your DataStage server for it to work.

Dynamic Relational Stage was leveraged for Peoplesoft to have a job to run on any of the supported databases. It supports ODBC connections too. Read more of that in the plug-in documentation.

ODBC uses the ODBC driver for a particular database, DRS is a stage that tries to make it seamless for switching from one database to another. It uses the native connectivities for the chosen target