There is no such thing as a cross-site duplicate in the Stack Exchange concept. There are several sites with a significant overlap in their scopes, and some amount of duplication is unavoidable. In general it is not considered a valid close reason if a question is already answered on a different SE site. Multiple version of the same question are even quite useful in some cases as different sites have different audiences and the answers can look at the same question from quite different perspectives.
Having a cross-site duplicate close reason would likely lead to confusion about the rules as it would suggest that they are generally against the rules.
The problematic part are not cross-site duplicates, but users cross-posting immediately without regard for the waste of time this can cause to the answerers. While I previously said that duplicates are not necessarily bad, such simultaneous cross-posts can cause users to waste time on answers that were already posted on the other site.
I generally close cross-posts when they are identical and without any effort to adapt them to different sites. If the question fits better to one of the sites, I'll close or flag the question on the other sites. If it fits equally well to all sites I tend to close the version on the site I'm a moderator on, as that is easier than flagging.