WordPress by default uses the same ‘edit_pages’ capability for both “edit” and “add new” buttons. In order to change this go to “Settings->User Role Editor->Additional Modules” tab and turn on the “Activate “Create” capability for posts/pages/custom post types” option. URE will reconfigure WordPress to use ‘create_pages’ for ‘add new’ button as a result.

Take into account that URE automatically grants ‘create_posts’ and ‘create_pages’ capabilities to the ‘administrator’ role only. You may need to re-check your roles (contributor, author, editor and others) to ensure users don’t lose ‘add new’ functionality where they should have it.