Generally, if the question is on topic on both sites, it requires the OP to want to have it moved. The moderators of sites I use with overlapping content seem to be generally very strict about this. They're also usually pretty good about not trying to hold onto something that the OP wants to have moved. This means that it's really the OP's choice which site it "belongs" on.
First, I would strongly discourage you making this sort of comment unless you are very versed in the target site's policies and you know that it would be acceptable there. The first rule of migration is "Don't migrate crap"... and that means two things.
If a question is poorly asked and would be closed for content reasons, being too broad, being too subjective etc..., the last thing you want to do is send it over to another site. Trust me, the target sites don't like that.
Don't migrate stuff to sites where it isn't on topic. Be certain that it's on topic before you suggest it, don't wait to find out that it's off topic when it gets closed on the target site.
Both of these cases cause issues both between the mods of the two sites and, if the OP doesn't have an account on the target site, it makes for a very bad first impression.
Now, once you're certain that the question is clearly written, well formatted, and would be on topic on a target site, how you write the comment becomes important. As a member of Movies & TV, we often get questions about subjects that are very popular on Sci-Fi & Fantasy. In the past, comments on these questions have caused some very negative reactions and long Meta conversations. So, be sure to be considerate of the local site before composing your comment. No site likes to have their users' abilities to answer a question well impugned.
Additionally, there's nothing wrong with a user deleting a question and asking it somewhere else (provided they're still able) and, if a question is closed as off topic, there should be no reason to not repost it on the site where it is on topic. If they are unable to delete due to there being answers with upvotes, then migration is, of course, the better choice.
When composing a comment, I think it's important to consider actually telling the user (particularly if they are new) about the site policies, albeit briefly. Consider something like
- Welcome to _____! While this is on topic here, the answer you seek may also be found on _____. If you visit that site and believe it is a better audience for your question, you can either delete this question from our site and repost it there or flag it for migration by a moderator. Please don't cross post the exact same question, however, as that is generally discouraged.
If they mention in comments that they would like to migrate the question but can't figure out how, explain how the "flag for moderator attention" flag works and go on your way.
If you use the AutoReview Comments Script, you could even add it as a default so that you don't have to think about it much.
You could even edit it slightly to use it for questions that aren't on topic so that the OP doesn't just get their question closed when there's another site it would be perfectly acceptable on.
As a final note, as you've probably seen in the questions you've linked, if the OP can target their question for both sites to emphasize the site's topic in the question, they can post the question on both sites but this is very complex and can be difficult to explain.
this can be OK, so long as the question is tailored to each audience on the different sites and is materially different in each case. Just to be 100% clear, copy-pasting a question across sites with no changes is considered abusive behavor. – Jeff Atwood♦ Jan 15 '11 at 3:51
