would RATHER - would PREFER - had BETTER:
differences and use

To talk about preferences, to give advice or to recommend an action, we can use 'would rather', 'would prefer' or 'had better', but there are differences in their use.

Would rather and would prefer are used to express preferences.
When talking about preferences, would rather and would prefer are interchangeable.
Had better is used to give advice, suggest an action or say what it is preferable to do.
Had better is similar to should but is stronger.

WOULD RATHER:
Would rather is followed by the bare infinitive (without 'to'): (She would rather leave now.)
- Alice would rather live in London.
- Tom would rather stay at home than go out this eveining.
- Chloe would rather call the landlord than send an email.
- We'd rather go on holiday in July than in August.
- They'd rather visit the old town than go to the museum.
- I would rather have my strawberries without cream please.
- She would rather starve than beg.

When asking someone not to do something, 'would rather' is followed by the past tense in the reply:
- "Do you mind if I smoke?" "I'd rather you didn't."

WOULD PREFER:
Would prefer is followed by the full infinitive (with 'to'): (She would prefer to leave now.)
- Hugo would prefer to live in Madrid.
- He would prefer to live in the centre of the city than in the suburbs.
- The children would prefer to go camping than stay in a hotel.
- I don't want to take the bus. I'd prefer to walk.
- Bill would prefer to take the train than fly.
- Some children would prefer to have a uniform.
- Shall we go to the cinema or would you prefer to do something else?

WHEN THERE TWO SUJECTS IN A SENTENCE: the structure changes
WOULD PREFER: Structure = subject + would prefer +subject + infinitive
-I would  prefer you to take a taxi home.
-I would prefer you to come on Friday.

'Would prefer' can also be used as follows:
- He'd prefer if you came in the afternoon.
- He'd prefer you to come in the afternoon.
- She'd prefer that you come on Monday instead of Tuesday.
- She'd prefer if you came on Monday instead of Tuesday.

WOULD RATHER: Structure = subject + would rather + subject + past tense
-I’d rather you took a taxi than walk home alone.
-I’d rather you came on Friday.

HAD BETTER:
Had better is followed by the bare infinitive (without 'to'): (You had better leave now.)
- You had better ask your parents for permission.
- Alex had better arrive on time for the meeting or the boss will be annoyed.
- It's unusually calm. We'd better check what the children are doing.
- You'd better tell the truth to the teacher.
- You had better do your homework before you forget.
- The restaurant is always full. We had better book a table.
- The traffic is heavy today. We had better leave early for the airport.