饿死你：to make you feel extremely starving. 困死你：to make you feel extremely sleepy. it's native speaking

饿死你：to make you feel extremely starving. 困死你：to make you feel extremely sleepy. Similar example: 气死你：to make you feel extremely angry. 乐死你：to make you feel extremely happy.

饿死你 means "starve you to death". 困死你 literally means "trap you to death" however I think the true metaphorical meaning is "suffocate you to death".