We had three candidates for a final round panel interview which involved a case study on fictitious work, but the job itself would relate to the type of work in the case study. One guy blew it off, so he was cut.
The final two candidates were neck and neck. The first candidate asked, “what did you appreciate about my presentation” as her main question. I mean, we answered truthfully. She did well with her visuals, and we liked the arguments she made. She also asked about our personal lives and what brought us to the company. I think these questions are just ok at best, as you can ask about these things even if you get rejected (although I know not every company will answer).
But the second candidate asked, “based on how this case study likely relates to the position, what is the biggest challenge one will meet in the first year here, and if chosen, how will I be supported to be successful?” This allowed us to give her specific details about what to expect and exactly how each of us in the room could support her. It also gave her a lot more information about the job without needing to offer to her at that exact moment. But, she was our number one pick, so she will hear from us this week.
Your mileage may vary, but definitely make sure you are asking questions that relate to the role. It places you in the best possible position to make an informed decision should you receive an offer, and it also might be the only relevant question the interviewer receives that day.