In theory NY and Hamburg instruments should be quite identical as they are based of course on the same design.
At first sight, you'll identify a NY Steinway by its somewhat different casing shape at some places. For instance the sides of the keyboard are sort of more "square" on an american instrument. The keyboard lid folds on a NY stweinway while it doesn't on a Hamburg model. I'm talking of course about the regular black concert finish. Also instruments of Hamburg production have a shiny polyester lacquer finish.
A few models are only produced in Hamburg: The A, C and the O for example.
I live in Sweden, Europe but last year I spent three months at the Banff Centre in Canada. That gave me the long awaited oportunity to compare apples... as I haven't come across an american Steinway in Europe... yet!
The NY instruments I could try and compare where a concert D, two B's, and a few S's. I found the B's had quite a poor sound compared to the B's I've played on in Europe.
The D was superb but not so different. I found the bass more clear and metallic somehow. Less round than what I'm used to. But I don't think that can be justified by the fact that it comes from the NY production line. Each Hamburg instrument is also different.
Incidentally, the NY keys had a slightly different shape.
Having talked to one of the piano technician, I learned that they use woods from different parts of the world in Hamburg and in NY, which is quite understandable.
I found the action different too, but it is very difficult to describe how, and again, I think that a skilled piano tuner could make a Hamburg action feel like a NY one and vice-versa. They are also, of course, build after the same design.
To really compare apples to apples you should go to a reseller, try and compare a new Hamburg D to a new NY D.
The instruments I tried in Canada had of course some parts replaced (like hammers) and had been fine tuned (the action), which is a normal part of a piano's life!
I hope I wasn't too vague!