You say that you cannot add columns in Prod, but maybe you can enable Change Tracking or Change Data Capture to track which rows that have been updated.
Else you need to compare column by column. This can be a bit laboursome when there are nullable columns involved. But here is a trick to find all changed rows:
SELECT ...
FROM src
FULL JOUN trg ON src.pk = trg.pk
WHERE NOT EXISTS (SELECT src.* INTERSECT SELECT trg.*)
This works because for the set operators INTERSECT and EXCEPT, NULL counts like any other value.
This answer is not particularly detailed of the very simple reason we know very little about your system, so I have to be generic.