A little search in Google Books indicates both are commonly used, but I cannot see any semantic difference:
Scholarly research can show how government subsidies benefit mostly the rich, not the poor, as is the case for gasoline subsidies in the Islamic Republic of Iran.
As is the case for most newly introduced high-tech services, crowdsourcing raises both hopes and doubts, and certainties and questions.
The important point to stress is that a radar imager, like a bat, principally obtains information as a function of distance from the instrument, rather than look direction, as is the case for optical systems.
Keeping confidentiality may result in future harm to some identifiable person other than the patient, as is the case with the prostitute and her boyfriend and the drug-treatment patient and his girlfriend.
Of the others, uncombined carbon burns with little or no flame, just as is the case with pure charcoal and coke.
My best guess is: with "for", it introduces the direct object for comparison; with "with", it introduces the scenario for comparison. So in practical terms, there's no salient difference between them. Do I get it right?