By telling "ought to" you suggest someone what is one of the last options one has or something that one can't easily avoid, for example, any longer. By telling "should" you suggest someone that something is good to be done or something that after all is meaningful. The difference is in importance you give when you say "ought to" or "should". "Ought to" wants to say that you think that it is more important something to be done. As well, "should" more expresses something than it is explicit. "Ought to" is more explicit, closer to a request than "should".

In general modal "verbs" should and "ought to" are used to say what we think it is right or good for people to do. In most cases, both should and ought to can be used with the same meaning. There is, however, a very slight difference. When we use should, we give our own subjective opinion; ought to has a rather more objective force, and is used when we are talking about laws, duties and regulations.

I second Gdl's comment. "Should" is the past of "shall", and is purely imagined. "Ought to" comes from "aught", which is an old past form of "owe". So, there must be something in reality to create an "ought to" phrase (eg. a reaction to a situation). As a reader, you can treat them as the same, but as a writer, this minor difference is the kind of thing you have to consider.