I got accepted in two different US schools for CS PhD programs. My prospective advisor/supervisor for the two schools are Professor X and Professor Y respectively. Professor Y was a PhD student of Professor X. Professor X has a lot of successful PhD students coming out of his lab and he is a heavyweight in the field. Professor Y is a tenure-track assistant professor but has really good recent A* publications. How should I approach this issue of choosing one of them?
(Moving from comment to answer)
This may not be true everywhere, but when faced with a similar decision I was told that the more established professor is more familiar with the department politics and how to get students graduated. Graduation should be a top priority, and if Professor X has a good track record of graduating students, that may be the best choice. Professor X also may have heavily influenced Professor Y's work, so it is unclear how Professor Y will work without Professor X's supervision.
Let me suggest that Professor X is probably safest, other things being equal. There is a danger in having untenured professors, like Y, as an advisor since their first priority is to earn their tenure and it can easily get in the way of properly advising students. You won't contribute much to their tenure, and so they need to focus on their own work.
Not every such situation is bad, but it is better to have someone who has the flexibility to help you succeed without the weight of an important career point looming. And if, for some reason, an untenured advisor fails to earn tenure, either during or after your studies it will cause issues for you.
I once had an untenured prof as advisor and found exactly this problem. I was far down the list of his priorities.
Inexperience can also be an issue in some cases.