The old Results tab allowed you to save and name results reports, and if you copied a survey those named reports would be present in the copy. With the new Results tab you can create a Results Dashboard, but when you copy the survey that dashboard is not present in the copy. It would have to be recreated.
Please add feature such that either the dashboard comes along with the survey copy, or ability to export it to a file and import into another survey (similar to the Advanced Reports .qrf functionality).