"Had better" implies that a person should because there's a negative consequence otherwise. You can think of it as a much more forceful "should." It isn't the same as "must" because there is technically still a choice, but choosing wrong leads to something bad. Examples: You had better study for the final exam. (If you don't study, you might fail.) You had better not mess with my stuff when I'm gone. (If you do, I will do something mean in return.) "Would rather" is used to show a preference, especially when declining a suggestion or invitation or when choosing between different options. Examples: 1. Would you like to go to the park? No, I would rather stay home. 2. I would rather put this money in a savings account than waste it on lottery tickets. You can also use "would rather you/he/she" when making suggestions/expressing a wish. This is much, much softer and gentler than "had better." Examples: 1. I would rather you do the dishes than wash the car right now. 2. I would rather he do his work than keep complaining. In these examples, there is no implied threat. Nothing bad is going to happen if the person doesn't comply (except, perhaps, annoying the speaker).