T-SQL Check another table rows if match delete them
I can't say anything about SSIS but in SQL you can check whether a whole row is identical to another (including checking for NULL values which can get rather complicated otherwise), using this technique, explained by @PaulWhite in his blog post: Undocumented Query Plans: Equality Comparisons .

For example in you case. "For any identical rows of table B and table A, delete those B rows":

DELETE b                        -- from table B: Customer_information
FROM Customer_archive AS a
  JOIN Customer_information AS b
  ON a.pk = b.pk
WHERE EXISTS (SELECT a.* INTERSECT SELECT b.*) ;


I have serious concerns though about efficiency when the tables are big - and an archive table by definition is going to be quite big. The a.pk = b.pk is not needed really, as the pk columns are obviously included in the row check of the EXISTS but I kept them for efficiency. Assuming that the two tables have the same primary key and that after a period, most of the archived rows have been already deleted from table B, the PK indexes will have very few matching values so the join will be relatively fast - and using the row checks only for matching pk values.