One of the features we are looking forward to in upcoming PostgreSQL 11 is the introduction of procedures via the
CREATE PROCEDURE ANSI-SQL construct.
The major benefit that sets apart procedures from functions is that procedures are not wrapped in an outer transaction and can have COMMITs within them.
This means it's not an all or nothing like it is with functions. Even if you stop a procedure in motion, whatever work has been done and committed is saved.
In the case of functions, a stop or failure would roll-back all the work. It also means you can see work in progress of a stored procedure since the work will already have been committed.
This is a huge benefit for batch processing. Batch processing covers a lot of use-cases of PostGIS users since a good chunk of
PostGIS work involves doing some kind of batch processing of data you get from third-parties or machines.