Simon, you could add the field definitions to the other table, then do an import from one table to the other
Even with Advanced's copy and paste, this only moves the field definitions. You would still have to move the data as a separate step in the process. Import Records is a good option if you have a one to one relationship.
There are other methods that use a looping script or Replace Field Contents that can also be used to move the data once you have set up fields in the other table.