PREFER / WOULD RATHER

2. PREFER / WOULD RATHER
2.1 PREFER TO DO and PREFER DOING
To say what you prefer in general
I prefer smt to smt else
I prefer doing smt to doing smt else
I prefer to do smt rather than (do) smt else.
Ex. I prefer this coat to the coat you were wearing yesterday.
I prefer driving to travelling by train.
I prefer to driver rather than travel by train.

2.1 WOULD PREFER
We use would prefer to say what smb. wants in particular situation ( not in general)
Ex. Would you prefer tea or coffee? Coffee, please.
We say `would prefer to do ( not doing)´
Ex. Shall we go by train? Well, I´d prefer to go by car.

2.2 WOULD RATHER (do)
= would prefer.
Ex. Shall we go by train? I´d prefer to go by car. / i´d rather to go by car.
I´D RATHER DO SMT THAN (DO) SMT ELSE.

2.3 I´D RATHER YOU DID SMT.
When you want smb to do smt.
Shall I stay here? I´d rather you came with us. → the structure we use the past, but the meaning is present or future.

Compare:
I´d rather cook the dinner now.
I´d rather you cooked the dinner now ( not I´d rather you cook)