My opinion is that questions should only be marked as duplicate only if they are on the same site. For example, if the same question is asked on the site for professional linguists and on the site for English language learners, it requires different answers and different level of detail. Perhaps the difference between MO and MSE is not that big, but there still is a difference. See also this discussion on meta.SO: duplicate questions on other SE sites?
If the two questions, which seem duplicate, are posted at the same time, the best option seems to be migrating one of them and closing as a duplicate. Such opinion was also expressed in a discussion on meta.MO: Close cross posts between here and MSE. If neither of the posts has answers and it cannot be closed as a duplicate, flagging for moderation attention has been suggested as the solution here.
If it is not cross-post, but simply two identical questions, then posting a CW-answer with a link to MathOverflow and some brief explanation seems like a good solution to me. This was suggested here: Closing questions as off topic if they have an answer on mathoverflow? Since this suggestion received 16 upvotes, it seems as a community consensus. (Although this was discussed before MO joined SE network.)