Back many moodle versions ago, I think one was able to edit the question from the "Edit Quiz" dialog box, and then "Save as new." I can't recall why, but Tim thought that this would work better from the Question Bank side. I respect Tim's position, and personally, have no problem with it at all. Maybe this is a "safety" feature, that too many people were not understanding what they were really doing when they "saved as new."
I am attaching a picture showing how to duplicate a question from the question bank.
I have found that on my moodle, duplicating a quiz that already has questions in it takes too long. So I prefer to set up the quiz characteristics first, duplicate it, then add the questions.
Also, (in moodle 2.9 or maybe even earlier) Tim improved the interface for adding questions to a quiz. I find it remarkably easy, intuitive, and productive. It is better than what I see in any other major LMS (thanks much Tim.) And I know how careful Tim was to listen to us users, test the interface, and then implement it. It would still be nice to have a "delete all questions" from the "Edit Quiz" interface, but I think that this feature is coming.