Delegate user permission to move users/computers between OU's in Active Directory

The common way would be to use the "Delegation of control" wizard which is part of Active Directory Users & Computers console snapin to grant the permissions on the OUs in question.

You would have to choose the object types you want to be affected. In your case this obviously would be the "user" object type. But there is no permission for "moving", you would have to grant object creation and deletion rights for the OUs in question instead. Doing so obviously would allow for user object deletions as well, but this is how it works - a move is a create/delete operation. See Microsoft knowledge base article KB818091 for a detailed reference.