When the question is "I have this problem" and there is already an accepted answer that solves that problem, duplicate questions can make it more difficult to find that correct answer. When used that way, the duplicate feature makes the site more helpful to everyone.
But in my opinion, the duplicate feature is widely over-used. Questions are marked as duplicates even when they could contribute meaningful information to a site. We really don't need to worry about disk space, so there's no reason to reject a question that could possibly make a site more helpful.
Here are two situations I can think of where using the duplicate feature might not be appropriate:
When the existing question is wider in scope than the new question.
Question A asks about X, Y, and Z, and gets an accepted answer. Question B asks about Y. Question B can technically be marked as a duplicate of Question A because the answer contains the answer for Question B. But there is obvious value to Question B getting its own answer. The next time someone is curious about only Y, they won't have to read through X and Z to find it.
When the existing question doesn't have an accepted answer.
The point of every question is to generate an accepted answer. If the existing question doesn't have an accepted answer, there's no reason to think that it's better than the new version of the question. We should be glad that people are willing to post the question in a new way, because it might draw attention to the question and generate a correct answer.