Both "prefer" & "would prefer" express the preference. This site said "You can use 'prefer to (do)' or 'prefer -ing' to say what you prefer in general" & "We use 'would prefer' to say what somebody wants in a particular situation (not in general)".

Would prefer prefer would rather?

Note that would rather is followed by a bare infinitive without to, whereas prefer requires to + infinitive. Would rather (but not would prefer to) is also followed by a past tense when we want to involve other people in the action, even though it has a present or future meaning.

How do you use would prefer?

We use would prefer or 'd prefer, followed by a to-infinitive or a noun, to talk about present and future preferences: I'd prefer to go by myself. Would you prefer a quieter restaurant? She'd prefer not to drive at night.