I believe it's the same for both provinces, 15% for new and used cars, but 8% only for private sales.
Now if we really want to go into details, I think the way Ontario calculates taxes is 7% GST of cost + 8% PST of cost, so:
cost * (1 + 0.15) = total
whereas in Quebec, it's the subtotal of cost + GST plus 8% of cost:
(cost * (1 + 0.07) ) * (1 + 0.08) = total
so you actually pay a little more in Quebec... I am not sure if it still applies this way, but it was years ago...