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 prefer to do meaning?

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)".

What do you prefer to do or doing?

But really there's no difference. Sometimes you have to use the gerund form when making a comparison. So you can't say She prefers to play basketball to to play chess. You can instead say She prefers to play basketball to playing chess OR She prefers to play basketball rather than to play chess.