You're far less likely to have problems with Canada than the US. In my experience, Canada accepts the concept of dual citizenship easily; the US reluctantly agrees that other nations accept the concept of dual citizenship, but they don't really believe in it themselves.
I have never, ever had any trouble entering Canada with my US id. In fact, I have a two brothers who are also dual citizens; one of my brothers had a minor issue entering Canada once and it was for a reason unrelated to his ID - that was the only time any member of my family had an issue entering Canada. I have twice been held up at the border, both times entering the US after visiting relatives in Canada, when I was seriously beginning to wonder if I was going to be allowed to re-enter the US.