Expressing preferences

 would rather/would sooner

 would rather/sooner + infinitive … (than)

We use would rather/sooner + infinitive (without to) to talk about preference. We can use it with than (+noun/infinitive) in affirmative sentences or with or in questions.

• I‘d  rather/sooner have tea, please. 
• I‘d  rather/sooner have tea than drink that coffee. 
• Would you rather/sooner have tea or coffee?

 would rather/sooner + subject + past simple

 We can use would rather/sooner + subject + past simple to refer to the present or future.

• We‘d rather/sooner she was/were with us now.*
• She‘d rather/sooner I picked her up after lunch. 
• Would you rather/sooner we went by bus or by train?

Note that we can use were instead of was with I/he/she after would rather + subject.
 

prefer

 (would) prefer + to + infinitive … (rather than/instead of)

 We use prefer/would prefer + noun or to + infinitive to talk about specific preference, i.e. what we prefer on a specific occasion.

• I would prefer to stay in a hotel near the airport. (or I would rather stay…)
• Most clients prefer to have breakfast in their bedroom. 

We can use prefer/would prefer with rather than or instead of to show the choices we have.

• I would prefer to be too early rather than be too late. 
• I prefer to go with dad instead of staying here with mum. 

Note that we use rather than + infinitive without to
 

prefer + -ing verb

We use prefer + noun or -ing verb to talk about general preference, i.e. what we prefer in general, on every occasion.

• I love running, but he prefers cycling. 

We can use prefer with to to show the choices we have. The word to is a preposition here, so if we use a verb after to, it should take the -ing form.

• He prefers walking to cycling. 

Exercises: 

https://www.test-english.com/grammar-points/b1-b2/would-rather-would-prefer/