But why expect differential brain drain between Africa and Asia

Here is a throwaway guess: because Asia is rapidly developing and Africa is not. If you're very smart and in (ex-Japan) Asia, you can stay and be successful (make millions / cure cancer / become a pop star / etc.) locally. It's a fluid growing environment. But if you're in Africa, your chances of local success are much smaller and, correspondingly, your incentives to emigrate are much higher.

I endorse Lumifer's reason. Other reasons would include less patriotism (as I understand, loyalties in much of Africa are to tribes/clans/families rather than a nationstate, religion, or ideology, so bringing your family abroad of going abroad to look for money would be less of a shift) and less perceived safety (e.g. apparently 75% of Ethiopia's skilled laborers moved abroad during its famines).