Having members in common with the UN does not automatically give it legitimacy. The UN does some good things, and does some things that are to give tinpot third-world dictators a chance to look respectable. The efforts involving the second are fine for trying to nudge countries into being more like the normal world, but should not be given any real authority over anything.
The question is, which camp does the ICC fall into? That question tells how much legitimacy it has as a court. (And I don't know the answer, so I'm not going to give one. All I'm saying is "It's like the UN" doesn't make it legitimate, at all.)
