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To be frank, using one or the other is not going to give you much noticeable benefit in search results - it depends on the links to the URLs and the content within them.
Generally speaking, a subdomain implies content that is "owned" by the domain name, but has a distinct purpose could not be covered within a single website. Whereas a subdirectory implies content that is a logical subsection of the domain name - part of a collection of content within that domain.
So for me, privacy.example.com (for a half dozen or so documents about privacy) wouldn't make any sense, unless it as a subject of big significance to example.com. www.example.com/privacy/ seems more logical.
As a counterexample, customers.example.com (for a customer portal) seems very logical.
There are technical issues too - typically subdirectories are quick to set up, and can be managed alongside other content on the domain. A subdomain is closer to a standalone site, with the additional work (but greater flexibility) associated with that. You can point a subdomain at an entirely different hosting company, for example.
Many people would see it as just a question of personal preference.