See clip from Attorney Rajiv S. Khanna's conference call video that addresses this question.
I would say that I think you should hold off. Don’t give up H-1 to go to H-4 EAD. There are couple of issues here. We don’t really know how far the government is going to go into investigating these cases - are they going to go to details of the H-1 status, if not it could be a simple matter to get H-4 EAD. If they start getting into status issues we could be looking at a protracted battle over the EAD issues.
People who are thinking of going to H-1 to H-4 EAD I would suggest hold off for a couple of months and let’s see how the government is dealing with the EADs and if they are asking for too much information you may not want to convert from H-1 to H-4 EAD.