Difference between "should" and "ought to"

Solution 1:

Semantically, there is no real difference between the two constructions, and they can be used interchangeably. I agree with you that "should" has become the far more common construction.

Even back to the Old English (and earlier Proto-Germanic), the words carry a nearly identical sense of obligation. As such, I'd be hard pressed to articulate even a minor connotative difference between the two forms in modern usage.

Solution 2:

Palmer (The English Verb) distinguishes three uses of should.

to lay a tentative obligation You should come to the party tomorrow. (ought to and should are completely interchangeable)
to express a probability They should be at their destination by now. (ought to is theoretically possible, but is rarely used with this meaning)
evaluative should It's strange that he should say such a thing. (ought to is not used)

Palmer, the English Verb/This forum

Solution 3:

The difference, in so far as there is one at all, lays with how much the speaker agrees with the obligation. I think.

You should go implies that the speaker (as well as possibly other people) thinks you should go.

You ought to go implies that, while there is clearly an obligation to go on your part, the speaker might not agree with it. Or at least reserves the right to not agree with it, even if he does think it's a good idea in the instant case.

This difference is very, very subtle, and may only exist in my mind.

Solution 4:

‘An A-Z of English Grammar and Usage’ by Leech and others says:

You can always use should instead of ought to.

In their ‘Cambridge English Grammar’, Carter and McCarthy tell us that:

Should is much more frequent than ought to, in referring to both what is desirable and what is likely.

Tags for clauses with ought to often occur with should, instead of ought

. . . . . . . . . .

Interrogatives and negatives with ought are rare; should is generally preferred instead

Elsewhere in the book they say: