E.g. very all-encompassing logging is generally good for security, and if the logs are stored in a secure fashion, there is also no security problem created. However, privacy suffers because one might log things one shouldn't log.

In the other direction, file and traffic encryption is good for privacy, and the less "permeable" you make it, i.e. the less readable for admins, system task, scanners, the better for privacy. However, for security, encrypting just for the user's eyes is a huge problem, because you cannot do malware scanning, you cannot do exfiltration prevention. Having users bring their own device into a work network is good for privacy, because those devices don't have central admin access, but bad for security, because same reason.