Add the Exchange 2010 server as PF replica partner for the Exchange 2003 server PF's:
If you are planning to have multiple Exchange 2010 PF servers, you can repeat the Cmdlet above to all of them.
Replicate the Exchange 2003 Public Folder hierarchy and content to Exchange 2010 server using ESM (Exchange 2003 System Manager), and then (if you have multiple Exchange 2010 PF servers), replicate the Public Folder hierarchy and content from the Exchange 2010:
As a last step, after you confirmed that all the PF have been replicated to the Exchange 2010, you can move all replicas from Exchange 2003 to Exchange 2010. The "move all replicas" will actually remove the Exchange 2003 replicas.
To move all Exchange 2003 replicas to Exchange 2010, which will actually remove the Exchange 2003 replicas:
Move Public Folder Content from One Public Folder Database to Another Public Folder Database - http://technet.microsoft.com/en-us/library/bb331970.aspx