rdxb,
I have to respectfully disagree with sophie on her strategy. While I think that, for example, your career goals and why Tuck, and how you would contribute to Tuck, should more or less remain consistent with the rest of your paper application, there is real room for you to further provide color to your overall application by giving them examples of challenges, leadership, strengths and weaknesses that expand upon or are different than what you mentioned in your essays.
Of course, you have to be careful with what you highlight and the examples that you choose. For example, regarding a challenge, you still have to ensure that the challenge is not a recent example - so that you can effectively show that you have grown from said challenge, etc. With weaknesses, you have to make sure that they aren't so serious that they are detrimental to your application.
anyways, just my 2 cents,
philly