Well if they are that similar, i would do the following.
1. Open the new Empty PCB
2. On the Empty one go to File open as Reference and open the Design you wannt to copy from.
3. Select everything you wannt to take over to the new Design. Use the Selection List if you need to.
4. With everything you wannt selected, go to Edit Copy to Clipboard
5. Go back to your Empty Desig, and go Edit Past from Clipboard
6. Now you may have to use the Parts Map Dialog that comes up when you do paste from Clibpoard. There you can do remapping, if you wannt.
There may be other better ways, but that is one that worked in the past.
Hope this helps