If we would hypothetically compare someone, who has similar high school rigour/extracurriculars, and grades and what not and one is in Canada, and the other is in the States, do both have similar chances to get into Princeton, or does the one in Canada require better stats/ national/international awards to be looked at seriously by admission officers compared to a domestic student, and if so, does dual citizenship make a difference?
I think this question overlooks a significant component of the application process - the personality of the applicant revealed through the application and essays. Primarily Princeton is looking for strong applicants who bring a unique strength to the university community.
Princeton is a private university so there is no strong incentive for them to choose domestic applicants over internationals. For that reason I doubt dual citizenship makes any real difference. Overall the international admit rate is lower than domestic but I am not certain this is true across all countries represented. For example, Canada (a country with likely a moderate number of applicants) may have similar acceptance rates to the US while another country with a very high number of applicants (ie China) may have considerably lower. Unfortunately these statistics aren’t published to my knowledge.
The education systems between the US and Canada are quite similar and well known to admissions officers. The disadvantage of applying from Canada is the lack of formal preparation for standardized tests, however some schools do offer this and if not, private companies can offer courses to prepare as well. After a certain threshold I believe it is the rest of the application - the EC’s, awards, essays, accomplishments and persona that connects the applicant to the ad coms. If you can make that connection through your app, where you come from is much less important.