A few things to consider:
I don't know how things work in Canada with respect to disability protections, but in the US, he would have more protection regarding any needed ADHD accommodations at the public school.
IB programs here tend to be very heavy on volume of written output, which can sometimes be a challenge with ADHD. Whether these demands will be higher or lower than at the private might be something to check out before your family decides.
The actual level of the curriculum in both would be good to check out, too, since good scores on IB exams frequently result in earning college credit or at least advanced standing. If you are leaning toward the private because you believe the curriculum will be even more rigorous and advanced, it would be good to ensure that this is in fact the case, and that there are mechanisms in place to provide similar opportunities for credit or advanced placement, so your child doesn't end up having to spend time and money repeating college coursework that had already been completed while in high school.
I don't really think that you are going to get poorly-motivated, low-achieving kids taking an IB program (particularly the high-level courses), unless you have a pretty darn stringent definition of motivation and achievement, so, if I were making this decision, I'd eliminate that from the list of reasons to consider one school over the other. Is the IB program where you are really known for having bad teachers? That seems strange.
Some research indicates that many highly gifted students learn best in environments where they have have the opportunity to engage with the material in a relatively less-structured way.
It sounds to me like your son believes he would be more likely to enjoy his experience at the public school and he would have more chance to follow some of his own interests (such as learning another language) and engage more with the family and with the community. You have to decide how much weight to give the quality of his experience as a factor in "good educational fit", and you might also want to consider whether things like already having a social network in place at the public school and being able to come home at lunchtime might decrease your son's stress levels and help with the organizational issues that sometimes go along with ADHD.
In retrospect, I don't think I did a very good job answering your question...
