From what I can tell, not much at all.
I would say that 'ought to' is something your grandmother would say, and 'should' is a word that the younger generation tend to use nowadays. It (should) just seems to have replaced it (ought to).
I agree; there's no substantial difference.
But, as in all of these 'no difference' answers, it's possible that you'll come across an exception one day. I can't think of any.
Oops, almost forget: quote quoted words. Please explain the difference between 'should' and 'ought to'.