Actually, I’d find it most helpful if there will be similar options to customize both (through a theme component or on the backend) So as an admin I could remove or add sections from either and items will not be repeated on the other component.
E.g. I could like to set up a reduced menu (but with admin tab) on some communities:
Then I wouldn’t need an Admin section on the sidebar. Or Bookmarks. Whereas in other cases it could make good sense to have them there.