From what I can tell from online forums and posts, one of the main focuses of BDD/ATDD seems to be on discussion and ensuring that the customer, developers, testers and other relevant parties are involved in the understanding what the system must do.
Question 1: Do BDD/ATDD stories replace the need for traditional requirement specifications, such as the those captured using the Volere Template?
Because the traditional requirement specifications are one of the key inputs for developers and testers, traditional requirement specifications tend to be comprehensive.
Question 2: Should BDD/ATDD stories also be comprehensive enough to allow a system to be fully tested?
Question 1: Instead of looking at this question as a black-and-white situation, we should better understand how these two requirements capture methods get along with each other. Writing a story in the BDD/ATDD methodologies, or in Scrum for example, does not imply removing the templates like volere off the table. If we take a look at the volere requirements specification here, we can see that most of the information regards to project-related issues, and the shell used for functional requirements is far from being different to a story. They just have different information, not exclusive one.
Question 2: Here we have the advantage coming from the methodology itself. BDD comes from TDD, we can more or less rely on the test-first oriented process to allow the team to test the system. But, as I mentioned in question 1, making a BDD/ATDD story more comprehensive is not a sin, and wouldn't compromise the general idea of the story. This would also prove useful when interacting with more experienced clients.