You're not looking at this the proper way.
Any reapplicant faces this
a) Any school you apply to as a reapplicant knows that not only did they not want you, no other school wanted you. To some taking you on with that caveat might make you "riskier", especially if you have rather competitive stats. The chances that you have flaws not readily apparent on the application are real in this case. That will make many uneasy. You really have to make a school "want" you as a reapplicant.
b) Youve already generated an impression at a school. And if a school forgets about that reputation, many if they are seriously considering a reapplicant will pull up your app from the first time you applied. So no matter what, theyll remember their first impression of you and it wasnt good enough. You have to change that impression. How do you expect to do that using the same essays? Your essays are a big part of your sales pitch. You already gave that sales pitch for yourself once; it didnt work. Dont use it again.
This is a good read for any reapplicant
http://admissions.med.miami.edu/md-programs/general-md/reapplicants
This is a good link that summarizes what you face. Perhaps the biggest thing to highlight is "The biggest mistake reapplicants make is reapplying too soon". Often times, changing essays is the first of many things a reapplicant will have to do to generate real interest if they apply again.