had rather
Would prefer (to do something); would be more inclined or willing (to do something). I had rather not talk to you right now. I had rather go see a movie, to be honest, but we can go dancing if you like.
had rather do something
and had sooner do somethingprefer to do something. (The had is usually expressed as the contraction, 'd.) I'd rather go to town than sit here all evening. They'd rather not.