We don't need the ability to close questions as duplicates cross-site. And as long as the questions aren't deliberate cross posts (i.e. the exact verbatim same post on more than one site), then neither question needs to be closed (unless the question has other problems).
For users who are able to cast actual close votes instead of flags (unlocked at 3k+ rep), it is already possible to vote to close a question for any reason. It's called "other", and you basically type your own close reason which is left as a comment on the post and in site statistics (unlocked at 10k+). Note that low-rep users who can only flag to close instead see the option "Blatantly off-topic (this question has nothing to do with X)". Closing the question with "other" doesn't function like a duplicate closure, but you could still use anyways. A real duplicate closure would have the duplicate at the top of the question and it redirects users that aren't logged in under some circumstances.
However, it would be a bad idea to close questions like this for one big reason (except in the case of a verbatim cross post, although I usually prefer closing the ELU copy): there's nothing to stop the other question on ELU from getting closed or deleted. There's nothing that most users here could do to fix this either, since you need privileges on ELU to reopen or undelete things there. There's also no way to tell that the two questions on different sites are linked at all from the other side (unless someone leaves a comment on the other question too and that comment doesn't get deleted).
Another reason is that each site caters to a different audience, so what makes a good answer is a little different. For example, a question that asks "why" might get an etymology answer on ELU, while on ELL it would be more appropriate to give a mnemonic or a good general rule.
As for other options, migrating old questions is usually a bad idea because it can dramatically affect people's reputation. Many of these old questions are also used as duplicate targets because the same old questions are always re-asked and re-asked time and time again on ELU. Furthermore, a migration of questions older than 60 days old can only be done by a CM.
With the existing features you have several good options:
- Post an answer on ELL using the information from ELU. Link to the other answer. If you copy what it says use quote formatting and mention who originally wrote it.
- Post a comment on one or both of the questions pointing to the other.
As for new features, I personally support expanding "question associations" to other sites. Right now this feature exclusively shows up on (English) Stack Overflow and points to questions on Russian Stack Overflow.