had better x would rather

[tom3m]

I'd rather go home.

I'd better go home.

Are example sentences above correct? If so, do they carry different meanings?

[emsr2d2]

I'd rather go home.

I'd better go home.

Are example sentences above correct? If so, do they carry different meanings?

Both sentences are correct but they do not mean the same thing.

I'd rather go home = I would prefer to go home.
I'd better go home = It would be a better choice for me go home OR I should go home OR I suppose I must go home.

Note that in your title "x" doesn't mean anything. You can use "vs" as a short form of "versus", or you could have called the thread "had better and/or would rather".

[Ju]

Are my understandings of the following sentences correcct?

Even though I'd rather go home and I'd better go home are both in the form of past tense, they still can be used in present situation.

eg.

Tomorrow, I'd rather to go home after the party.
Tomorrow, I'd better to go home after the party.

Thank you.

[bhaisahab]

Are my understandings of the following sentences correcct?

Even though I'd rather go home and I'd better go home are both in the form of past tense, they still can be used in present situation.

eg.

Tomorrow, I'd rather to go home after the party.
Tomorrow, I'd better to go home after the party.

Thank you.

They are not in past tense.
"Tomorrow, I'd rather to go home after the party." "Tomorrow, I'd better to go home after the party."
These are present tense referring to the future and they would be more natural with "tomorrow" at the end.

[Odessa Dawn]

Please note:

"Had better" is often simply pronounced as "better" in spoken English.


Source: ENGLISH PAGE - Had Better

What does the underlined part mean?

[Chicken Sandwich]

What does the underlined part mean?

NOT A TEACHER

People sometimes leave out "had" or "'d". So you'll hear both "This better be good" and "This had better be good." The first one isn't grammatical, but it's common enough.

Also compare:

You'd better not go out tonight.
You better not go out tonight.

The weak form of "had" in "You'd" is so quiet that it is often not heard at all.

[Barb_D]

In the US, "I'd rather" is "I would rather" not "I had rather," at least in my experience. I tried to find a reputable site that told me that I was wrong or that I was right, and didn't get that far.

[5jj]

They are not in past tense.
"Tomorrow, I'd rather to go home after the party." "Tomorrow, I'd better to go home after the party."
These are present tense referring to the future and they would be more natural with "tomorrow" at the end.

A rare occurrence - I do not agree with bhai. Technically, I'd (I had) [better] is past tense and, for many people, would is the past-tense form of will. Whatever you feel about would, neither would [rather] nor had [better] is a present-tense form.

They are however, used for present-time preferences/suggestions.

[Chicken Sandwich]

In the US, "I'd rather" is "I would rather" not "I had rather," at least in my experience. I tried to find a reputable site that told me that I was wrong or that I was right, and didn't get that far.

I can't find a credible source either, but judging from the books in which "had rather" is used, I'd say that "had rather" is rather old-fashioned/archaic. At least, that's what I gather from searching through Google Books.

[5jj]

In the US, "I'd rather" is "I would rather" not "I had rather,"

It's the same in BrE.