As a dual US and Canadian citizen with both passports, how do you?
Travel with both passports. If in an emergency you suddenly had to go to the US, and you only had your Canadian passport with you, then its going to be problematic. As for which passport to enter with when travelling to other countries, enter with the passport that gives you visa free entry to that country. If both passports allow visa free entry, enter with the passport that has an embassy near the city where you are visiting. If neither of those facts apply, it does not really matter which passport you enter with.