Would rather vs Would prefer

Negative form for WOULD RATHER -- would rather + not + bare infinitive (verb1)
• I would rather not tell you.
• She would rather not eat.
• He would rather not go to work today.

Negative form for WOULD PREFER -- would prefer + not + infinitive (to + verb1)
• I would prefer not to play a game.
• They would prefer not to face the problem.
• She would prefer not to invite him.