Build two sections in the dashboard with one report each.
For first section, give the permission for the groups to export. And this section should have the report links >> Export enabled.
For second section, DONT give the permission for the groups to export. And this section shouldnt have the report links >> Export enabled.
So, the group who has the permission to view the section will be able to see the section with Export option enabled and vice versa for the other section users.
Hope this helped/ answered
For me this is rather a work around. Is there no privilege for the export function?
For me it sounds quite natural that some users should not have the ability to export any data. I just had a meeting with a customer yesterday and we discussed this.
Doubling the report just creates a huge maintenance overload.