The result is the same - the person or object is completely wet through. However, drench makes me think of pouring water over something, and soak makes me think of something sitting in water. Or any liquid, for that matter. Interestingly, they're connected to the words drink ("to give drink to") and suck, respectively.

It is exactly the same. There is no difference. (As far as I know - native English speaker). :) Although, used a verbs -- "to drench something" (eg."I drenched the car") means to make it very wet. "To soak something" (eg. "I soaked the plate.") means to leave something in water for extended time.