Of course all major cities are so like each other that it isn't even funny. A-M could be New York, or London or Madrid or Paris or Berlin or Washington or any major city. I feel the differences between major cities are much akin to identical twins getting their hair dyed and this is why you will always see something of home in A-M

My take on it, as an English reader, and bearing in mind just what he's playing off, is that Ankh-Morpork's got nothing to do with New York; rather, New York has its origins in the same city Ankh-Morpork does.

Ankh-Morpork is really nothing to do with New York. A-M is an evolved twist on London as was. But so, in fairness, is NY (or so Pterry says) - this is why so many Discworld cities have an A-M flavour while not being A-M; this is why so many Real World cities have a flavour of London. All cities, in a Platonic sense, are echoes of one city, Pterry tells us, and that city is Ankh-Morpork.

Or, if you'd rather, the man's not that familiar with America or New York, but he is familiar with London as is and as was, and also with the tropes surrounding fantasy cities. Mix the two, and you might get something resembling New York, but it's not actually based on New York. It's more a case of reality resembling the fictitious natural progression of that city.

(He also gets a lot down pat, because the man's an excellent satirist, and there's a lot of readily available source material.)

I agree. I think that Pratchett has simply hit upon something to do with the peculiarities of being human. People are really more alike than they think (or would like to believe, in some cases).
But that's merely my two cents =)