Well....it's actually quite hard to describe. I was hoping that someone here has tried a Snappy Pizza before and therefore can relate to what I'm talking about. Anyway...here goes!!!
The crust is around 5mm thick and is soft. A slice will sag quite a bit when you pick it up. The edge of the crust is also soft and springs back when you squeeze it (it's a bit like puff pastry in it's constituency).
Most dough recipes I have tried (including the NY recipe on this site) are quite good (they have mainly used bread flour), but are not the same (no disrespect intended!). They generally seem to result in a coarse 'bread like' crust whereas the Snappy crust (which does call itself New York style BTW) is 'smoother', not quite so chewy, and has large air pockets in it (if that makes sense?).
I realise the above probably isn't very helpful!!, but I'm not really sure how else to describe it.