Error Backing Up Database using drush: Call to undefined function drush_sql_dump_execute()
I would bet almost 100% that you're using drush 7 or higher.  The function drush_sql_dump_execute doesn't exist in drush 7.  Support for drush 7 was added as of CiviCRM 4.5.5 - see CRM-15567.

That link suggests that drush 6 has the same problem.  I would recommend using mysqldump until you're upgraded.