Packaging your functions in an extension has the advantage that it allows you to call remote functions when using the postgres_fdw Foreign Data Wrapper.

PostgreSQL 9.6 added extension function pushdown as a new feature allowing functions to be executed on the remote side as long as the extension is registered with the foreign server. This avoids having to fetch all the data from the remote side to execute a function locally, see https://www.postgresql.org/docs/current/static/postgres-fdw....