Cursory and perfunctory both suggest something lacking, but they fall short in different ways.
Cursory means quick and not thorough. The problem is limited attention or shallow review. If you give a document a cursory look, you looked at it fast and probably missed details.
Perfunctory means done with little care, interest, or sincerity. The action may be completed, but it feels mechanical or indifferent. A perfunctory apology sounds like someone is apologizing only because they have to.
A simple contrast helps:
- A cursory glance is brief and superficial.
- A perfunctory apology is unfeeling and routine.
Use cursory when the main idea is speed and lack of depth. Use perfunctory when the main idea is lack of care or sincerity. Sometimes both can apply, but the emphasis is different. One is too quick, the other is too automatic.