Rather and Prefer are words used to show a choice from
different options.

For example:

Would you rather eat pizza or pasta?
I would rather eat pizza.

Would you prefer to eat pizza or pasta?
I would prefer to eat pizza.

STRUCTURE

The structure of these sentences are the same except for one
small difference:
Would Rather is followed by a base verb and Would Prefer is
followed by an infinitive.

Subject + Would + Rather + Base Verb

I would rather live in a warm country.
I would rather go to a different restaurant.

Subject + Would + Prefer + To + Verb

I would prefer to live in a warm country.
She would prefer to meet on Monday.

Not comes before the verb with both rather and prefer.

I would rather not go to work today.
I would prefer not to play a game.

Take a look at this conversation to see some examples of
would rather and would prefer:

Alex:
Would you rather stay home and cook dinner or go out?
Betty:
I’d rather go out. I am pretty tired today, so I don;t want to
cook. What about you? Would you rather stay in or go out?
Alex:
I’d prefer to stay in, but we can go out if you would like.
Betty:
That would be nice. What type of restaurant would you like to
go to?
Alex:
I’d prefer to go somewhere quiet.
Betty:
Really? Not me. I’d rather go somewhere fun, maybe even
with some live music.
Alex:
But I thought you were tired?
Betty:
I am, but not too tired to have some fun.
Alex:
Well, I’d prefer not to, but…..OK.