Cross posting is a bad idea. It's rare that exactly the same question is on topic on both sites. Having the same question (and potentially the same answers) on two separate sites is splitting the knowledge. Stack Exchange is all about having one place where people can find the answer to their question.
At the very least you should be tailoring your question to each site, emphasising the parts that are particularly relevant for that site over the rest of the question. What would be ideal is that you wait for a while and then ask a new question using the information you've gained from the answers to the first on the most appropriate site.
If you really think that your question would do better on the other site then flag it for moderator attention. While migration to a(nother) beta site is discouraged - there's no migration path - it does happen.