There is no notion of cross-site duplicates. If the questions are on-topic on both sites, both should be retained. Please link to the other question in a comment or answer on each side, so that askers, potential answerers and future visitors know where to find the work that already exists on the subject. The idea behind keeping both versions is that the questions are reaching two different communities and may receive different answers. If you've answered on one side and your answer would be appropriate on the other side and doesn't duplicate an existing answer, feel free to repost it on the other side (adapting to the different community if necessary).
Of course, if the question is off-topic on one site, it should be closed as off-topic.
If the two questions are identical and posted by the same user at the same time, this is a cross-post (or more precisely a multi-post), and these are strongly discouraged. Here the reason is that asking two identical questions duplicates efforts on the answerers' part.