When I was younger, I looked at everything from a prism of productivity. Will music lessons help me to become a better presenter? Will the job at top-100 university help me to find a better position in the future?
Of course, I translated my productivity-focused vision on the choice of lab for PhD. So I looked for such information: does a professor have a paper in "Nature"? How many grants are in the lab? How many PhDs have recently graduated here?
Now with my work and life experience, I would ask questions of different nature. I would go philosophical. Here are my top-3:
Why do your PhD students do this project?
How do you feel about your field of research?
What is the point of this?
This time, I would rather listen to the reaction and emotions of a professor, instead of looking for pure facts. I would try to see a human behind the papers.
How about you? If you have a PhD, what would you ask differently? If you are thinking about joining a lab, what questions are you planning to ask?