If the user has permission to add entries to global feeds, but the user does not also have permission to create pages in at least 1 area, then the user will only see a button to Add Existing Page.
(Secondary answer: A global feed will appear at the top of an area if the user has permission to view the list of contents of the area, and if the area counters show that at least 1 global feed exists inside that area. If this was not working on your older site it might be that the area counters were wrong for some reason, or the feed was waiting for moderator approval, or it was actually a personal feed.)