Choosing PhD advisor between Professor X and an Assistant professor Y who was a PhD student of the professor X
(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.