Entry requirements to the USA are based on your country of citizenship (e.g. which passport you hold), and becoming a PR does not change that. If you do not need a visa to travel to the USA, you need an ESTA to travel by air, but not by land.
https://help.cbp.gov/app/answers/detail/a_id/1192/~/canadian--citizens%2Fresidents%2Flanded-immigrants-entering-the-u.s.
"Residents (PR) of Canada who are landed immigrants need a passport and visa to enter the United States, unless they are a citizen of a country eligible for the Visa Waiver Program (VWP). If they are a citizen of a country eligible for the VWP, they are only required to have their valid passport - coming by land or sea. If coming by air, they will need to have advance approval to travel through the Electronic System for Travel Authorization (ESTA). To obtain a list of countries eligible for the VWP, please reference the Department of State Web site."