Would rather & Prefer
Prefer and would rather are both used for expressing our preference or choice between different options. They have the same meaning, but their grammar forms and rules are different from each other.
My father would rather drink tea than (drink) coffee.
My father prefers drinking tea to (drinking) coffee.
My father prefers to drink tea rather than (drink) coffee.
She'd rather buy a gold ring than a silver ring.
She prefers buying a gold ring to a silver ring.
She prefers to buy a gold ring rather than a silver ring.
I'd rather watch a match than go to the cinema.
I prefer watching a match to going to the cinema.
I prefer to watch a match rather than go to the cinema.
Would rather does not take a noun afterwards, but Prefer can be used with a noun.
He would rather
have a house in the town. (he would rather a house.)
I'd prefer a house in the town.
When we want somebody else to do
something
we use pronoun with prefer (me, him, them...)
I'd prefer him not to smoke
She said she'd prefer us to arrive no later than nine o'clock.
but we use subject with would rather (I, you, we...)
I'd rather he didn't smoke
She said she'd rather we arrived no later than nine o'clock.
For the past events:
I would prefer to have stayed at home rather than have (gone) out last night.
but
I would rather have stayed at home than (have) gone out last night.