SQL to find record with a value in one table but not another table

Assuming your IDs do not change in either table so that ID 100 in Address always points to ID 100 in Address_Backup:

  SELECT * 
    FROM Address_Backup
     WHERE ID NOT IN (SELECT ID FROM Address) AND Code = 'OTHER'

using NOT EXISTS

 SELECT * 
  FROM Address_Backup AS B
  WHERE NOT EXISTS (SELECT 1 FROM Address WHERE ID = B.ID) AND Code = 'OTHER'