While all of those places do make good pizza, I personally think it is a different kind of pizza than Pete's, I don't really know how to explain it, there's no good adjective to use to describe the two, at least that I can think of. I guess artsy is the only word that comes to mind when I think of 2 Amy's and some of the other places similar to that whereas Vace is more Italian styled pizza, if that makes any sense at all.
I think Pete's is more New Haven inspired pizza than anything, because it can't be real New Haven pizza since they can't install coal ovens in DC(I think, I might be wrong). I say inspired because I know one of the owners worked in a pizzeria in East Haven for a time, and I think that might be where the New Haven comes from, because although it does not resemble Sally's or Pepe's or Modern, it does resemble some other pizza places AROUND New Haven in Hamden and other places(such as Eli's and Olde World) that use a more traditional pizza oven like Pete's.