The Priority Criteria for Selecting The Principal Advisor
There are multiple facets to this.


Quality of research
Reputation "rubbing off"
Quality of mentoring
Amount of work and stress
Personal ties
I've surely forgot something.


The major problem is that some parts of this might be more important for you than for me and vice versa. So, the basic thing is to decide what do you actually want from this position:


Get a PhD and leave
Qualify you for further academic life
"Parking lot" until you have found a better position in the industry
Have fun
Whatever.


This impacts a lot on the "weights" on the above qualities. Further, in my experience it's never a broad choice, but rather a sequence of binary choices. Say, the junior PI approached you first, you declined, the gossip in the staff room got to the star PI, he did not suggest you a position. It's an extreme example, but it's not "should I go with PI A, B or C", it's "should I take an offer from PI X or not".