Choosing between an older, prominent supervisor and a younger, junior supervisor for PhD I'm searching for a PhD position in theoretical physics. My question is:

Should I do my PhD with a prominent professor who is 60 years old and does not care too much about their students or with a junior professor who is not famous and does not have published too much papers, but cares too much about his students and is very supporting and nice professor?
I'll talk from my own experiences, as in my career I have worked with both kinds of supervisors: I was under a really famous professor, who did not care about his coworkers at all (to the point of not knowing my name) and with a little-less famous person (who became a professor only after we started cooperating). The former was a complete disaster, as he was not interested in my work at all, did not offer any advice (and you, as a junior researcher would need advice from the wiser ones) and was unpleasant in personal contacts and eventually ceased all communication, thus hindering my academic progress.

The latter offered interesting guidance and by the end helped me to settle down in academia by recommending me to a position.

After all, you do not work with names, but with people. Even younger professor is probably much more experienced than you and can share some of it to you.

Also, bear in mind that this is only my personal statement and your mileage may wary. While reading questions here I, for example, got the impression that names play quite big role in academia (not in work, but on recommendation letters, etc.), so you have to take that into account as well.