ought to es como el should, sí. expresa algo que deberías hacer, pero no es obligatorio, es una sugerencia.
i ought to/should visit my grandmother when i'm in London on business next week. [i'm going to London for another reason, but while i am there, it would be a good idea to visit my grandmother, although it is not necessary].
you ought to/should see a doctor about the headaches you've been having [giving advice].
might se usa para expresar duda. no estás muy seguro de lo que vas a hacer, ej. tomorrow i might go shopping with my friend (but i'm not sure).
where are you going on holiday this year?
- we don't know yet, but we might go to France.
también expresa una sugerencia ej.
you might want to have a doctor look at your sore eye (it would be a good idea for a doctor to look at it)