As promised I would like to explain that I don't perceive "brands" of schools and my way of valuing schools to send my children to has, if anything, an anti-brand bias. Having gone to public schools most of my life, and having found them adequate, but variable, I had no reason to suppose that I would pay more money to send my children to a private school. Annandale was a new public school when it first opened, was the closest public primary school, and had a "catchment area" that was quite well off. All factors that made for an easy choice of school for my first three children - a total of 18 child years. The closest public High school had been ruled out for consistent word of mouth criticism for lack of a suitable bullying policy. Not content with hearsay associated with these kind of criticisms, I counted as most reliable data points students and parents that I knew, that had direct experience. All of the data pointed to the principal being the key to the issue. Had the principal left before our eldest had finished grade 5 or 6 - we could well have changed our mind.
From that point, the primary motivation became a fear of our kids being zoned into an unacceptable school, or being in limbo on a waiting list not knowing until too close to the starting date. A second motivation came in the form of our 4th, who was due to start prep the year after our first moved to high school. We were scrambling to see which school had better programs for autistic children. A third motivation was the struggle of doing pickups and drop-offs to geographically distant schools. A fourth was being able to get our children into instrumental programs, which were free but oversubscribed in Annandale.
Private schools, especially Catholic ones, have early enrolment deadlines, which means early acceptance of a place there. Informal surveys of all the special needs childrens' parents that we knew noted that Annandale was not catering well for special needs children. Ryan Catholic has a large primary and high school close together which made pickups/dropoffs easier. Instrumental programs at Ryan were also a lot more accessible, although more expensive. A clinching factor for doing the entire switch was the catering for large families. Fees for four children at the school was less than double what it would be for a single child (which makes it about one fifth the price of the Grammar/Cathedral brands) AND the large catholic population of the school doesn't give you stares if you have any more than a couple of children.
So although we are spending a little more money than we would with public schools, the difference is much smaller than most people imagine.
I had a line-ball decision after grade eight and grade nine because my oldest wanted to change to Pimlico. The clincher was that the motivation was primarily to be with friends than any particular academic or otherwise benefit. I am really not sure if the decision was right, but the balance of various risks was better to stick with the school she had been in.