If the DOJ were inclined to bring charges against Wilson, they most certainly would NOT have to "show the same evidence." Prosecutors are under no obligation to do what the St. Louis prosecutor did here by showing all of the evidence (inculpatory and exculpatory), and most do not.
That said, I think a Federal prosecution here is highly, highly unlikely. Not only would such a prosecution have to overcome Wilson's (very strong) self-defense argument, but a federal prosecution would also need to prove that Wilson acted specifically because of racial prejudice. Even if the DOJ could prove that the shooting was not justified (e.g., in a hypothetical world where Brown did not, in fact, present a threat to Wilson), that alone would not be enough to sustain a federal prosecution.
If DOJ finds one single police associate of Wilson’s....that says he made racist comments at work or while at some bar...then they could introduce that guy and make a minimum effort at some case. That’s the only way that this would work, and I doubt such a witness exists. But even with such a witness....you’d have to sit through several weeks of testimony and see the same evidence as before. It’s not like the DOJ can just invent new fresh evidence of this case....there’s simply nothing much else. All DOJ is doing is keeping the family spirits up a notch in hopes of “something”.