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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.
In light of your comment that the older professor does not publish with his students, I'd recommend looking at the careers of their respective former students. The best predictor of future performance is past performance, so assess the two potential mentors in terms of their past success in setting their students' up for productive careers. In making that comparison, also take into account that the illustrious, older professor has likely had some of the best students working with him. If they haven't succeeded, I would steer clear.
Your post is quite vague and it's hard to know what you mean by saying this 60 year old professor doesn't care about his students. Is he not supportive, does he not reply to emails, does he not give good feedback, is he too busy, is he going into retirement? One can only assume it's one or some of these.
By the sounds of things you have already made your decision. Though experience is highly important in academia, the same importance could be lent for how much a professor inspires you. This younger professor may not be prominent, but every professor has to be young [or younger] at some point and if you like this younger professor, and feel excited at the prospect of working with him, choose him. If he inspires you, you are likely to produce a far superior quality of work than if you work under this older, more experienced professor who, to you at least, appears rather dry and unmotivating.
I was the first PhD my advisor had produced; and I could not have had a better experience. My only warning would be to make sure your younger professor has published in journals where you would like to publish, too, and preferably more than just one or two papers. Experience in writing for those journals is something you want, because typically you need to publish a few papers to prove elements of your dissertation are actually "an original contribution". At least that is how it was judged at the two universities I attended; just a PhD committee's agreement that it was original and a worthy contribution was not considered sufficient; acceptance in a peer-reviewed journal was the criterion.
Anyway, a younger professor with no PhD graduates yet will pay more attention to you, and may be close to your age (within 10 years) so treat you less dismissively than the older professors, and in my experience may have more energy, working more hours, and be more available to you than older professors. I was able to discuss my project with my advisor nearly every day, probably 4 out of 5 weekdays. I know other candidates that went much longer than that. I know one candidate that chose the department head as his advisor, and got one hour a MONTH with him, and after a year of that worked up the courage (or enough frustration) to switch to a new advisor and started all over with different research. Mostly wasted a whole year.
Added: It can also be true for a young professor seeking tenure that successfully graduating a PhD is a plus mark for his tenure case, in 3 or 5 years. Unlike a tenured older professor, this is another incentive for the younger professor to pay attention to your progress and keep you on track.
