I'm skeptical about the need for such a site: fragmenting the community in this way seems to me like a big negative, so it would take some big positive effects to make up for that. The proposal is currently extremely vague (the entire content consists of "If in any doubt whether a question would be better posted at Mathoverflow or Mathematics then post it to Postgrad Mathematics instead" and the example question "Which Cayley graphs are planar?"), and it would need a lot more detail to make a compelling case.

What's the fundamental motivation here? I can believe someone might hesitate to post graduate-level questions to MO, out of fear that they will be closed with a suggestion of trying MSE, and I see this as a problem with MO. On the other hand, I don't see why the new site would be an improvement on MSE. The advantage of asking on MO instead of MSE is that MO has a larger user base of grad students and faculty, and it's possible that the new site would develop such a community. However, that would take a lot of work, and I'm not convinced the new site would have an advantage over MSE in this respect.

Quoth Henry (emphasis added):

I can believe someone might hesitate to post graduate-level questions to MO, out of fear that they will be closed with a suggestion of trying MSE, and I see this as a problem with MO.

I completely agree. I think that graduate and postgraduate level is exactly what MO should be aiming for.

I agree with Henry, MO should be a welcoming place for good graduate student questions (indeed that's essentially how the site started). Similarly m.SE is happy to have questions at any level (advanced questions don't get huge attention there, but they often get answered nonetheless).

I respectfully disagree with Kevin's comment. The same question is likely to receive very different (good) answers on the two sites. Briefly: If you want a concise answer that assumes you already are familiar with (or willing to learn on your own) any well-known notions that come up in the answer, MO is probably the site to ask on, even if you think the question may be "too basic." Some people may find good MSE answers condescending (even if that is not the intent), while others may find good MO answers to be filled with incomprehensible jargon.

I've had both complaints (mentally) at various times, but on the whole, I find that MO tends to be more helpful to me than MSE does.