Unless a single user cross posted the same question (different discussion) there is no such thing a cross site duplicate. They are either in scope or out of scope, if they are inscope they should be open.
You can't assume that all users will be on all sites. Each site has to stand on its own merits and you have to treat each site as a separate community.
If a question is inappropriate on one site, users now have alternate places to go with it. It's a nice convenience if moderators choose to transfer it for them. If it turns out to be a duplicate, let the other community handle it with the means already in place. If the first moderator happens to spot it as a cross-site duplicate, it can simply be closed and the original poster can decide how to rework the question if they want to try it on another site.
In the edge case where the question is appropriate on more than one site, leave it on both sites and let the users of each community benefit from the information. Source Robert Cartaino at Meta.SE
