Take two base classes A and B which
are similar but are preferred to be
distinct. Each has a sub class (A' and
B') which add the same functionality
and members to their respective
classes.
This is a bit of an odd place to start from. If it were me, I'd be looking to change this part of the design.
Assuming that's not reasonable, for whatever reason, I think Decorator is about the best you can do to avoid code duplication.
You will need to create the subclasses, A' & B'. And you'll have to declare the added methods and properties in each. Those members should delegate to members of another class that can implement the common functionality. An instance of that class will be contained in both A' & B'.
This really only saves you duplication if the implementation of those common members is significant.