I believe both private and public beta aim for the same level. The FAQ is the same: “Chemistry - Stack Exchange is for scientists, academics, teachers and students”. I also believe Nick T’s answer during private beta is still a very good criterion for judging whether a question is too easy for us.
To expand on this a bit, we want to strike the right balance between:
- “experts only” (in which case, we can hardly gain any traction… see theoretical physics and astronomy and lessons to be learnt there)
- popular science (cue “mentos + coke”, “mentos + sprite”, “mentos + Dr.Pepper”, … questions),
- students’ tavern (“how do I know if a ligand is classified as strong ligand field or weak ligand field?”)
Nick T's criterion can be formulated in other alternative ways. For example, I'd be more tempted to describe it as a “no general reference” policy. Also, we should not that this is in addition to other important and more generic criteria, such as questions being fact-based (as opposed to argumentative) and not being overly broad.