Multi-posting, i.e. posting the same question on several Stack Exchange sites, is strongly discouraged as a matter of network-level policy. In the specific case of CS and CSTheory, multi-posting should be forbidden.
If a question is asked on CSTheory, is a generally good CS question but is not research-level, it should be migrated to CS. I expect that when CS graduates, it will become a migration target for CSTheory; in the meantime CSTheory moderators can migrate the question.
Conversely, if a question about theoretical CS is asked on CS and turns out to be research-level, it may be migrated to CSTheory (by a CS moderator).
I expect that we'll get incoming migrations from Mathematics and Stack Overflow and Programmers.
As long as we're in private beta, it's too early for any migration. Generally migrations should wait until the target site has moderators (this is not a hard-and-fast rule). The private beta is intended to seed the site with good questions as well as establish some minimum participation; we should stick to original questions (original for Stack Exchange, I mean) for the duration of the private beta.