You delete a post when the content no longer adds anything to the site. Posts are closed for a variety of reasons:

Exact Duplicate: Look at the content of the duplicates and see how much they differ. It's a judgment call. If the question is yet-another duplicate (asked over and over) it may not be worth cluttering up the system further. But if the wording provides another way for people (search engines) to find the content, leave it. It will act like an index reference pointing to the right post:

How do I do [thing]: see "How do I do [other thing]"

Off Topic: Almost always delete it. Off topic usually says "it shouldn't have been posted here in the first place."

Subjective/Argumentative: Judgment call. Decide between "fair question but we discourage this so we couldn't let it continue" (i.e. keep it) and "this is nothing but a 'broken window' and we should get rid of it" (i.e. delete it).

Broken Window: It’s pretty clear now that the broken windows theory applies to community sites as well. The theory is that minor forms of bad behavior encourage worse ones: that a neighborhood with lots of graffiti and broken windows becomes one where robberies occur. I was living in New York when Giuliani introduced the reforms that made the broken windows theory famous, and the transformation was miraculous. And I was a Reddit user when the opposite happened there, and the transformation was equally dramatic.

Not a real question: Almost always should be deleted. Closing it gave the author/community ample time to fix it up. If it wasn't reopened by this time, it should probably go.

Too localized: See off topic.

You delete a post when the content no longer adds anything to the site. Posts are closed for a variety of reasons:

Exact Duplicate: Look at the content of the duplicates and see how much they differ. It's a judgment call. If the question is yet-another duplicate (asked over and over) it may not be worth cluttering up the system further. But if the wording provides another way for people (search query results) to find the content, leave it. It will act like an index reference pointing to the right post:

How do I do [thing]: see "How do I do [other thing]"

Off Topic: Almost always delete it. Off topic usually says "it shouldn't have been posted here in the first place."

Subjective/Argumentative: Judgment call. Decide between "fair question but we discourage this so we couldn't let it continue" (i.e. keep it) and "this is nothing but a 'broken window' and we should get rid of it" (i.e. delete it).

Broken Window: It’s pretty clear now that the broken windows theory applies to community sites as well. The theory is that minor forms of bad behavior encourage worse ones: that a neighborhood with lots of graffiti and broken windows becomes one where robberies occur. I was living in New York when Giuliani introduced the reforms that made the broken windows theory famous, and the transformation was miraculous. And I was a Reddit user when the opposite happened there, and the transformation was equally dramatic.

Not a real question: Almost always should be deleted. Closing it gave the author/community ample time to fix it up. If it wasn't reopened by this time, it should probably go.

Too localized: See off topic.