I wouldn't put too much stock into the notion of black hole creation being like a mini big bang. The big bang itself, unlike the supernovae that precedes a black hole, wasn't an explosion. The univere's initial expansion was less like a "bang" and more like a "vrooooosh".I suspect the moment of creation of a black hole looks a helluvalot like a big bang -- from inside the black hole. Including inflationary expansion.
Still, I think the clearest argument against relating the big bang to black holes is that the former was, necessarily (else we wouldn't be here), a relatively low entropy state, while a black hole represents a maximal entropy configuration. Black holes look much more like the end of the universe than the beginning.