Would it be too dangerous to have a supervisor who is very famous but more than 70 years old? Here is my analysis:
1, they are more established, even Noble Laureates, everyone in the field knows him
2, maybe they have more time to discuss with you? (not sure)
1, they are not that active in research. Their recently publication are not that productive than the younger big guys. Thus your publication may not be that productive than those working younger big guys.
2, their health condition may be a problem. You may have to change to another supervisor in the middle of your program (I know one guy did this). Even if you successful finished the phd under him, when you come to look for faculty position, he may not be able to help you. (At the beginning of career, a lot of young AP still need to collaborate their supervisors .)
3, the group size maybe too small, maybe inter group collaboration would be limited.
What do you guys think?