I grew up in Toronto. My 3 kids variously went to public school in Toronto, private school in Toronto, public school in the US and private school in the US. I’ve taught at private and public schools in Toronto and in the US.
There’s many factors that go into the cost/benefit analysis of private vs public K-12 school. Some of the pros of private school are small class sizes, individual attention from teachers and admin, students are screened for ability and social characteristics, college counselors are available and attentive.
The young adults that I know who came out of K-12 private schools seem to be more self-assured to me. They are more socially competent. Public schools don’t have the ability to turf out trouble makers. Private schools do.
At the secondary level, the material would be more challenging and engaging in a private school than in a public school, especially the level of the schools you listed in your post. The teachers are more likely to have a PhD or masters in the subject matter. There will be 12-16 students in a class rather than 30-40. It is far easier to teach and learn with the smaller class size.
As to why families will choose University of Toronto, Queens, Waterloo, Western, McGill over similarly ranked US schools? #1 Cost. Tuition at the Canadian schools runs $7K-17K CAD vs about $75K CAD at the US schools. #2 Where a student wants to live. Most students do not go very far for university. It is not easy to get a visa to stay and work in the US after undergraduate studies. #3 If a student does want to study in the US, it makes a lot more sense to do so for graduate studies when the cost for US schools becomes similar to Canadian schools and visas become more attainable.
In my experience, Canadian parents will pay the money to send their kids to HYPMS over say University of Toronto, but not so much for schools outside of HYPMS. Students want to go where their friends are going