We have a similar issue since we live in the US, but my daughters and I all have dual citizenship. We have looked at and applied to multiple schools in the US as well as multiple schools in Canada, and I currently have one daughter in university in the US and one in university in Canada.
If you want to work in the US after graduation, then there might be an advantage of either going to university in the US or going to one of the better known schools in Canada. Certainly McGill, Toronto, and UBC have very strong reputations in the US. Waterloo does also for computer science. I know multiple people who graduated from one of these four schools for undergrad and now work in the US. Several are in very senior positions in their various US employers. Several also went to highly ranked universities in the US (including Stanford and Princeton) for graduate school after doing undergrad in Canada.
If you want to work in Canada after gradation then going to school in the US can be a major problem. Canadian companies seem to prefer to hire from Canadian schools. This was a big problem for me a number of years ago, and is one reason that I am still in the US several decades later.
There is a huge difference in cost, and a huge difference in the transparency of the process.
In Canada you get accepted mostly or sometimes entirely based on grades, SAT or ACT scores, and to a lesser extent references. This makes admissions relatively predictable and in our experience very low stress. If you have something close to straight A’s and SAT scores well over 1400 then in our experience you pretty much just pick a school and go there. Since cost is so reasonable and similar at different schools you get to decide based on where you want to go, not what it is going to cost. Some universities are asking for essays and ECs but we didn’t happen to apply to them, so the process was quick and easy. In our experience responses (acceptance letters) come back relatively quickly. One minor issue that we did notice: Since my daughters went to high school in the US, a couple of schools missed the fact that they are also Canadian citizens and along with their acceptances sent information on how to apply for a visa and on cost for international students. A quick phone call and a fax straightened this out very quickly (as a Canadian you would pay Canadian tuition).
In the US you get accepted due to a wide range of factors which are very difficult to predict. I have seen students with an unweighted 3.5 get accepted when students with unweighted 4.0 from the same high school were turned down from the same top university or college. In the cases that I am aware of the students with the 4.0 either had identically rigorous courses or more rigorous courses and also had significantly higher SAT scores (in one case by 350 points in the two part SAT). One result of this lack of predictability is that students apply to a larger number of schools.
We don’t have experience with need based aid. Merit based aid is available at Canadian schools and at some US schools and not at other US schools. In our experience merit based aid might or might not reduce the huge difference in price between the US and Canada, but Canadian schools are likely (assuming that you don’t qualify for need based aid) to be less than half the price of US schools, sometimes much less.
If you are a Canadian (dual) citizen who was born in the US or who has lived in the US for a long time, you might want to ask admissions staff at McGill about “Canadian born abroad” pricing. It is an amazingly good deal if you qualify (inexpensive even by Canadian standards).
In my opinion there are very good universities in both Canada and the US, and you can get a very academically demanding and very good education in either country. Canada doesn’t have anywhere that has quite the same reputation as MIT or Stanford or Harvard, but the top schools are excellent in either country. As one example I think that my daughters are both getting very good educations at a very similar academic level in the two countries. Other than price and difficulty in applying, the differences between their schools are more related to the size of the school than to what country it is in.
One daughter was interested in small schools (what we would call a liberal arts college in the US). Let me know if you might be interested in these as this could result in a lengthy post just on its own.