One thing you absolutely need to do is reach out to the graduate students they’ve advised in the past and ask those students about their experiences with the respective advisors. Nobody will know what the situation will be like with each advisor better than their previous students. Some questions you might consider asking the students include
1. What is the advisors personality like? Did you feel like you could talk to them about things outside of research or were things strictly professional and academic?
2. How present was the advisor/how much “hand-holding” was there in research during the course of your PhD? Were you just given papers and told to find research topics on your own or did the advisor meet with you frequently (weekly, biweekly, multiple times a week, etc) to discuss research topics, ideas for proofs, and papers in your field?
3. How much did the advisor connect you with people they knew in academia/research/industry? (Some friends of mine have advisors that don’t do much to get students connected with people they know in their field. Other friends of mine however frequently get invited to zoom/Skype meetings their advisor has with research collaborators to help the student form connections at other institutions. This can help a lot with finding a position in your desired career path after graduating)
4. How approachable is the advisor in general? Are they intimidating or are they very friendly and easy to talk to? (This is similar to question 1, but id suggest asking this question explicitly as well since early in your PhD, being comfortable asking questions and telling your advisor that you don’t know something or that something is unclear to you is hugely important for success)
5. What was/is your favorite thing about working with the advisor and what was/is your least favorite thing or worst experience with the advisor? (This can help you get an idea of what the best times and worst times will be like with either advisor. In particular, knowing what the bad experiences are like can be a huge factor in deciding who to go with since one very bad incident can have a really big negative impact on your feelings and work success during your PhD)
6. Is there anything you wish you knew about your advisor before you started working with them?
And lastly, my go-to question whenever I finish any sort of interview or meeting with people where I can ask questions is
7. Is there anything I should be asking that I am not?
This last question can help act as a catch-all since there will almost certainly be questions that the grad students know of that don’t occur to students applying for PhD programs. The past or current student that you’re talking may just say “no, I can’t think of anything” to this and that’s fine.
Hope this helps