Which is formal?

[afzal21]

I am confused with the following structures, that, which is formal

sub + had better + verb + ext or, sub + would rather + verb + ext as for example:You had better stay here or, You would rather stay here.
I had better go now or, I would rather go now.

[5jj]

It's not a question of formality, but of meaning.

I had better go = it is advisable for me to go; it would be better if I went.
I would rather go = I prefer to go.