Looking into the Cambridge dictionary, I see both sentences are correct. The difference is in the intentions of the responder.
In the first sentence John expressed disapproval, in other words he expressed different opinion or preference. There is a kind of comparison between two opinions, example:
Sam: I'd like to wear the white shoes for this festival. John:No, I’d rather wear the black shoes.
However, " suggest that..." after "rather" is a polite way to introduce an opinion. Instead, John may respond more boldly and directly:
Sam: I'd like to take this exam next year. John: I'd rather take it this year.
In the second sentence John have not expressed different opinion, he just shared his opinion as "very" or "to a large degree", example:
I did rather well in my exams.
I've got rather a lot of work to do at the moment.
He boobed rather badly by getting her name wrong.
I think my husband is the most handsome man in the world, but I realize my
judgment is rather subjective.
I've had a sort-out in the bedroom - it's looking rather better.
I heard something rather worrying at work this morning.
Jane has rather a sharp tongue, I'm afraid.
The correct usage of "rather" in the second sentence is to be included between parentheses"", in this case rather will be inserted in the sentence as an explanation.
For instance, I'd suggest, rather, that..." was mentioned in this ebook.