Well, I think a lot of the "comparing schools - questions" come from people already in the private school orbit who's child(ren) are applying out to another private school. Often, especially if the current school is supportive and helps guide the applicant, it is highly likely the child will obtain offers from most of the schools to which they are applying.
If your child is graduating from a school that traditionally ends at 3rd or 4th or 6th or 8th (most common years) the current school usually recommends the next step schools to which your child should apply based on their current academic achievements and overall behavior and abilities. This group of schools consists of those that would fit your child well and to which the child should be able to gain admission. The first school's reputation is also in play here so they have a real motivation for getting graduates into next schools that will work for the student - just like private high schools are judged based on where their seniors matriculate for college and then judge by those same colleges and universities by the high schools graduates who have matriculated in the past.
In this scenario, the group of schools which your family is considering is also a much smaller group than that of someone who may be applying to privates for the first time. In the former, your child has weight of the current school behind them. It makes a very big difference in one's odds of getting an offer of admission - it is less of a crap shoot.