I have recently been admitted to a few PhD programs, and have to decide where to attend. One of them has a massively famous professor (over 50k citations, 'Reuters Highly Cited Researcher'). Other potential supervisors at other institutions are still quite famous (~15k citations). Could anyone share some potential differences in my experiences if I work with someone who is that famous, or not? The group sizes/number of current students are all comparable.
I knew somebody who started a PhD with a super-rockstar in Computer Science. He told me he met with his advisor thrice in a year or so, once (a short meeting) when defining the thesis topic, once crossed him in a hallway, and came across him at a conference. It turns out the rockstar was on the road almost 24/7. He changed to a not-so-famous advisor, and was much happier.
Agreed with vonbrand's answer, but I would like to add one thing. If the rockstar professor is nearing retirement, he could actually have a great deal of free time to supervise you.
I took a topics course with a "massively famous professor"; there were only two of us in his course. After classes every week, he invited us into his office for casual conversations about his life in grad school and in academia - and what were the biggest surprises in mathematics during his younger days. We learned that he hadn't taken on a student in many years. My classmate convinced him to advise him on his thesis. The problem given to my classmate is an especially tough one, it seems, but he is thrilled to be working with this famous, yet gracious, professor.
OTOH, if the professor that you are thinking of is still highly active in research, he will likely be on the road often -- he may not even attend many of the classes that he is assigned to teach for the semester. I've also experienced this, too.
Good luck with your decision.
I recommend you perform the following experiment. Choose several established people in your field whom you admire. Look up who their advisors were. See whether or not they were, themselves, ``famous''. Draw your own conclusions.
As indicated in a couple comments, using citation counts (solely) to judge what kind of advisor someone is a bad idea. First, citation count isn't an accurate representation of how good a research is for many reasons, one of which is citation counts vary greatly within subfields. Another is that they change over time and comparing citation counts of younger versus older researchers is unfair. What would be better is to visit the groups and get a feel for them if possible, and find out where the advisor's former students ended up.
However, here are some possible things to consider with rock star versus cover band advisors:
A famous advisor is likely to have a stronger group, particularly if they are at a more prestigious institution. This can benefit you in many ways (learn more, explore better ideas, stronger collaborators). Cf: University rank/stature - How much does it affect one's career post-Ph.D?
An eminent researcher may have a more refined/greater perspective on the field, which you can absorb by osmosis.
An eminent researcher may have better connections, providing more opportunities and "advertisement" for you. This includes benefiting from the chance to meet many established researchers coming to see your advisor.
An eminent advisor may give you better problems/give you better tools to solve problems.
A rock star advisor may not have much time for you, and may not even remember your name. Therefore, you may be expected to be more independent (but this expectation is not limited to rock stars).