I don't see a lot of people jumping on this post. Perhaps this has been long settled by the regulars. Fact is, there are actual differences between pianos made in the two locations today. The U.S. factory does not export outside of North America, ie. the New York facility only manufactures for North America. Steinway Hamburg supplies the rest of the world (Europe, Asia). Hamburg Steinways are shipped at 443 Hz, New York 440 Hz. American 'ebony' (black) Steinways are laquered. Hamburg Steinways have a high-gloss polyester finish. New York actions are presently made in the U.S. facility. Hamburg instruments use an action made by Renner to Steinway specs. In the past there were other differences concerning the actions and hammers. The variation in action and hammers could affect the sound, of course. Everything else above is a matter of logistics or cosmetic.
Steinway's two locations build different models as listed here:
http://www.steinway.com/html/showroom/cat_1models.html
The sizes for Steinway are S, M, L, O, A, B, C, D, small to large. As you can see, the O, the A, and the C are presently made only in Hamburg. These are models that were all previously manufactured and sold in the U.S. and fill the gaps between the model B and D, and B and L. The O has a round tail as opposed to the same-sized square-tailed L, which has more soundboard in the area close to the bass bridge. In Larry Fine's 'Piano Book,' (4th ed.) you can read when these 'Hamburg' models were discontinued in N. America.
So, what's the same? Answer: Everything else, including the scales for the models made at both locations.
The website above uses the word 'identical' in reference to the Hamburg and N.Y. question, which I interpret as 'identical within quality control limits'. That is a good aim for an international manufacturer of high standards, but in reality, no two pianos can be 'identical' in all respects, even if manufactured at the same facility.
I've read that renner hammers are hard, whereas the hammers made in the American Steinway factory are soft and always need to be treated with hardening chemicals to properly voice the instrument. My dealer here said the Hamburg Steinways are preferred by most international recording artists and have a warmer tone. I remember a Steinway dealer from Chicago in rmmp (was it Steve Marcus?) who said that all the artists who perform there use the U.S. models except for Daniel Barenboim, who specifically requested a Hamburg piano. Many pianists rave about the old O's. I've never heard raves about an L.
I remember reading an account of a Horrowitz concert where Gidon Kramer (violinist) attributed the 'harsh' sound to H's American Steinway. I deal regularly with three German O's and have heard many performances on various German D's. In the right hands, they are all wonderful instruments. Pianists tell me every Steinway is different and spend a lot of time looking for 'the right one' when they buy for themselves. My experience with the U.S. instruments is from over 10 years ago, and at the time I wasn't paying too much attention to subtle differences in piano sound. I've read that the U.S. factory was plagued with quality problems during the 60's, 70's and 80's, (extensive post about that here a week or two ago, but I can't find it, sorry), but from what I've deduced, the Hamburg branch was not as affected by these problems.
Its said musical tastes differ, but IMO, generalizations concerning nationality are often made on the basis of very little information. Big 'American' sound, warm 'European' Klangkultur. I beleive one needs to listen to the individual artist. Many things have contributed to the formation of an 'international' pedagogical-, technical-, sound-, and aesthetic- ideal. With a flood of recordings, our ears are used to everything these days, wherever we live.
IMO, two pianos can even come from the same factory and have very different playing characteristics and sound, depending on how they were shipped, stored, used/abused, played and especially how they were serviced after the sale. Steinway keeps the New York/Hamburg difference as small as possible, but two pianos are never going to be 'identical'. Thus, playing up the difference based on the manufacturing location and making generalizations is faulty reasoning. BTW, there are some great books about the history of Steinway, the leading piano manufacturer of the 20th century. A great piano success story indeed. It all starts with a German Klavierbauer by the name of Steinweg...