It highly depends on the context, which that includes the question and your own privileges.
Let me first re-iterate the goal of closing:
Questions that need additional work or that are not a good fit for this site may be put on hold by experienced community members. While questions are on hold, they cannot be answered, but can be edited to make them eligible for reopening.
So closing is, for me, a way to start the work with the OP to get their post into shape, and that is guidance that I promote in a chat room I visit to help in moderation efforts.
To start this work towards re-opening we need to establish how future visitors will benefit from this question if it turns out to have more value then only being a duplicate.
Let's assume for the sake of this answer that the duplicate will not be gone soon (a zillion views, mega up voted, a post history of delete/undeletes)
If the new question is a blatant duplicate but uses different/more up-to-date or maybe even historical wording, close the new question as a duplicate.
If you have a gold badge for one of the tags on the question, close vote as a duplicate. This will prevent FGITW answers.
If the new question isn't adding anything new in the perspective of that duplicate, close vote for a correct reason.
In all these case don't forget to use your other moderation options you have at your disposal like editing, (down) voting, delete voting.
The benefit of having new off-topic questions that are closed against the duplicate is improving the search-ability of these questions. If more variants turn-up in the Google search, the more likely the future visitor will find the duplicate and not ask a new question.
By having those new questions only closed as off-topic you have a higher probability that new duplicate questions will keep turning up, because the duplicate is not found by the Google-ers.