Practically the US expects that you enter the US on a US passport and leave the US on a US passport. Right now, the former is easily enforced (incoming customs controls whether on US soil or preclearance) while the latter is not because the US generally does not have exit customs controls.
Right now I only have one passport (US), in a couple weeks I'll have my Canadian. Practically speaking, I don't generally need either passport to enter Canada or the US because I use NEXUS - that's the document (NEXUS Card) that I use in the machine at Preclearance re-entering the US, and in the NEXUS kiosk at Canadian customs entering Canada. Both the US Global Entry and CBSA NEXUS computers know that I have both citizenships (and will know I have both passports - I have to visit the office for them to add my Canadian passport). If I go by land and present my NEXUS card, they would see that document too. And by land, they're fine with an enhanced drivers license (issued by a few states, requires proof of US Citizenship, has an RFID chip for US CBP to read).
I don't know what will happen if the US implements proper exit controls, if the choice of travel document when checking in will matter. Practically at customs with my name & date of birth info they can reconcile my travel regardless of either passport I pick. But as far as the passport number that is transmitted by the airline to CBSA, I don't know if US or Canada cares
You can use your NEXUS card as the document that the kiosk reads at GE machines, but only at Canadian preclearance locations. I use my NEXUS card at GE preclearance because the bottom of the photo page (machine readable zone) is pretty beat up on my US passport and GE/airline kiosks have a tough time reading it. (When entering the US at non-preclearance locations, I tap the button on the screen to type my document number on the GE kiosk touchscreen instead). Assuming the US is aware of both citizenships this is fine, although I always carry my US passport anyways (in case I get sent to secondary) - if you get secondary inspection, generally US CBP and CBSA want to see your passport anyways. (The GE/NEXUS computers are separate from the ones that secondary officers use, and seeing the passport can help in verifying possession of the document and reviewing exit/entry history).
If you naturalized as a Canadian citizen, then under U.S. law, you have committed a
potentially expatriating act. A
potentially expatriating act can lead to actual expatriation (loss of U.S. citizenship) if the act was committed
with an intent to relinquish U.S. citizenship. The courts have been clear that behaviour can establish intent in regard to
potentially expatriating acts. The key to having your behaviour determine your intent to maintain U.S. citizenship is to behave in a way that an American citizen would behave. That generally means: entering/exiting/transiting the USA with a U.S. travel document (including what you provide to airlines for preclearance); never providing a foreign travel document to an American peace officer (an enhanced Canadian drivers' licence/ID exempted); never applying for a U.S. visa or eTA. In short, behaving in ways that only an American would behave (e.g., renewing a U.S. passport, voting in U.S. elections) and never behaving in ways that an American would not (e.g., publicly denying being an American, neglecting to include "USA" on [foreign] forms that ask your citizenship, public statements that you moved to Canada because you didn't like the President).
When travelling through American airspace (direct flights between Canadian cities are exempted) you should provide your U.S. travel documents to the airline to be transmitted to Government. Canada won't care if you use a U.S. passport, but the U.S.
may care if you use a Canadian passport, and
may use it as "proof" of intent to relinquish U.S. citizenship when you committed the
potentially expatriating act of naturalizing as a Canadian citizen.
Dual citizens are not popular in America and are often viewed with suspicion of being unAmerican. Most Americans are unfamiliar with U.S. nationality and immigration laws, but ardently believe that dual citizenship is illegal and immoral. It is a widely held belief that living outside the U.S. for over five years will result in an automatic loss of U.S. citizenship. Targetting dual citizens for expatriation would be very popular among sectors of the electorate and dual citizens would receive little sympathy from the rest of the electorate. My advice is to tread carefully and make one's intentions consistent, straight-forward and crystal clear.
