To be safe, I would re-write the essays. You can keep the "spirit" of the essay the same, but I would definitely put in the time and effort to make them different. Otherwise you run the risk of looking lazy.
(Not saying that you are...I've got what feels like dozens of old essays I wish I could reuse, and frankly I see nothing wrong with it but this is what I've been told by ADCOMs)
At the bare minimum, I would change the first sentence. That'll throw them off a bit. 😛