Here's the way this has been explained to me by a diamond moderator in the past (my recollection may not be 100% true, so any misrepresentations are a mistake).
Basically, questions that were asked on SuperUser, which are on-topic for SuperUser, should not be migrated to other sites solely by virtue of the fact that they are also on-topic elsewhere, even if that other site is more specific. There has to be another reason.
Now, if the question is sitting on SuperUser and not getting any attention -- like if it's been here 5 or 6 days and no one has (usefully) commented or answered -- then migrating is more likely to be approved. Keep in mind that we also try not to migrate poor content to other sites, and sometimes when we're in doubt, we'll ask a moderator of the other site if they want it. If they say no, we're unlikely to debate it further with them; we'll either close it on SuperUser or leave it open, but we won't migrate it if they ask us not to. We want to be a good role model for the rest of SE, and not force our unwanted questions upon other sites.
TL;DR: We should not be migrating questions to other sites if any of the following are true:
- The question is low quality (not answerable, too broad, X-Y problem, etc.)
- Moderators from the other site (diamond or even 10k users), who we've asked about the question, have told us they don't want it migrated
- The question is medium- to high-quality, unambiguously on-topic for Super User (irrespective of the topicality on other sites), and is getting feedback from the community, or has an active bounty
- The OP of the question specifically meant to ask it on Super User
- The question is extremely old and the OP hasn't visited the network in a long time (at least several weeks for both time measurements) -- because the OP will be unlikely to revisit the question on the site it's migrated to and accept an answer
The question should be migrated to other sites if and only if all of the following are true:
- The question is high-quality, or you are willing to edit it to make it high quality (in fact it is good practice to edit away any problems at all that you see in the original question before migrating, or clarify things that the OP left out by asking them in comments)
- The question has received very little attention from our community (few views/answers/questions) and/or the quality of the comments and answers has been low, and the OP is unsatisfied with the responses so far; OR the question is unambiguously off-topic for Super User
- If you have any doubt whatsoever as to whether it's topical on the proposed destination site, you have asked a veteran user of that site (e.g. in chat) whether it's OK to migrate
- If the OP is responding to comments or participating in chat, the OP agrees that they want it migrated
- The question would likely be closed or become a tumbleweed (neglected question) if it remained on Super User