How to choose a proper contraction "it's not" versus "it isn't"?

Question

I'm aware that both it's not and it isn't are contractions of the same phrase, it is not.

Till today, I was convinced that choosing them depends on desired emphasis. This way, choosing it's not allows one to make an emphatic stress on not:

It's NOT my fault!

...and other than that it's just a matter of style, not grammar.

Recently, I was watching Monty Python's "Argument Clinic":

M: An argument isn't just contradiction.
A: It can be.
M: No it can't. An argument is a connected series of statements intended to establish a proposition.
A: No it isn't.
M: Yes it is! It's not just contradiction.
A: Look, if I argue with you, I must take up a contrary position.
M: Yes, but that's not just saying 'No it isn't.'
A: Yes it is!
M: No it isn't!

I was surprised they have never used it's not during the whole sketch.
This confused me a lot as it opposed my prior understanding: two people contradicting each other would rather use it's not.
More than that, at 01:42 they have used you did NOT and then you DIDN'T, which must indicate that the latter is more pathetic than the former.

So, how to choose a proper contraction between "it's not" versus "it isn't"? Which one is more emphatic, and how come a contracted variant looks more pathetic than the expanded one?

Answer 1

‘An A-Z of English Grammar and Usage’ by Leech and others suggests the following:

With be, use the contraction + not (e.g. That’s not right).

With have and modal auxiliaries, use the verb + n’t option, e.g. hasn’t, can’t.

The authors go on to say that forms such as She isn’t hungry, as opposed to She’s not hungry, are less common, and that forms such as I’ve not met him, as opposed to I haven’t met him, are much less common.

The authors don’t say on what basis they make their recommendations, but they are likely to be based on frequency of use. There doesn’t seem to be any difference of meaning or emphasis. I would just add myself that a contraction such as I’ve not met him sounds more formal, perhaps because of its lower frequency.

Answer 2

As you've said, placing emphasis on a word is a matter of desired emphasis which is a matter of personal style rather than rules. I think you could make exactly the same point by putting stress on isn't (It ISN'T my fault!)

In the Python sketch, the emphasised word is 'it' not, 'not'. Part of the humour in the sketch is the repetition of it - 'It is.' 'No, it isn't.' 'Yes it is.'. This wouldn't have carried the same impact if the humour was based on, perhaps, the back and forth of 'It's not', 'Yes, it is.' 'No, it's not.'

Also, they can do this with a number of forms of the sentences in the sketch, for example 'It can be.' 'No, it can't ...' The humour wouldn't carry through these sentences if the emphasis had been used on the 'Is/Not' structure.