Nope. I went to a rather renowned APSIA school for my undergrad and it makes very very little difference. Academically, universities recognize APSIA schools as top international affairs programs but professionally, it's worth zilch (and I say this, after having had a few related internships).
I would recommend talking to profs you trust in the program and asking them directly. Foreign policy wise though, both schools are great,
though I would argue that U of Ottawa has the bigger names (with some exceptions at NPSIA like Saideman).
I'd agree with the previous commenter that there's really no "best" program, it all comes down to what feels like the best fit.
Welcome Masa! And congrats, apparently NPSIA only admitted 2 international students this year. Both programs have a lot to offer, it all comes down to what your academic interests and professional aspirations are (NPSIA might be a better fit for those who want to work for the Canadian government, etc...) . Toronto is most definitely more expensive, but it's a much more interesting city as well.