I'm hesitant to try and speak to such a general question as this one, but I've decided that I'll give it a try to the extent that I'm able. You can take my opinion with a grain of salt; it is a big question and may not be able to be answered, but I have a few observations on the matter.
My collecting focus is on North American pipe artisans. I'm also involved in a pretty extensive interviewing and writing process that is resulting in a series of articles and a book on North American carvers.
I'm not sure that this is a question that CAN be answered in accurate terms. I believe that it can only be answered impressionistically as any reasonable answer requires inspection and observation of many different artisans' work over a period of time.
As is the case with most artists (and artisans), it is easier to talk about specific artisans. One of the difficulties is that there is a great deal of both artistic and technical influencing going on and the spheres of influence are not limited to North America. For example, H. Tokutumi has had a momentous impact on the work of many NA carvers, including Todd Johnson, Jeff Gracik, Michael Lindner, and Brad Pohlmann. Tokutumi's influence on Johnson has been adapted through mutation and experimentation and passed on (through his aesthetic filters) to people like Brad Pohlman and Jeff Gracik. Jeff Gracik is very open about Jody Davis' influence on his work. Jody has likewise influenced people like Michael Lindner. My point here is that the strong professional and interpersonal relationships between these various artisans cannot help but produce aesthetic influences along with technical advances.
Here are my observations (and opinions):
1. If I were to characterize the aesthetic vocabulary and shaping strategies of North American carvers, I would describe their shaping aesthetic - overall - as "muscular" in comparison to other Europeans and the Japanese. There is a certain "heftiness" and "beefiness" in both the lines and in the design; take a look at Larry Roush, Jim Cooke, Brad Pohlman, and Brian Ruthenberg and compare their approach to proportions and lines to the Danes and you'll see what I mean. There's a lot of testosterone in the overall aesthetic vocabulary.
2. As a rule, the pipes from most American carvers are larger in both size and smoking chamber capacity. Obviously, there are exceptions but since Americans like larger pipes, the carvers work toward satisfying that market demand.
3. North American carvers tend to produce more idiosyncratic and organic shape lines that suggest a certain "freehandness." These pipes are not so much freehands as they are evolved expressions of classically derived forms. Sometimes the derivation is not particularly transparent, but our inability to see it does not mean that it is absent. In a way that is not unlike jazz, American pipe artisans approach classical shape and line and "riff" on them. This is not so much a rejection of classical forms as it is honoring them through the act of departure. You have to know the rules to break them successfully.
4. The blasting style of most North American pipe artisans is considerably both more detailed and craggier. This is due in no small part to the use of smaller glass bead media. This media produces a distinct style of blast that stands in pretty stark contrast to most European artisans.
5. Some artisans working in North America - like Tonni Nielsen and Alex Florov , for example - create pipes that are more strongly aligned with the Danish and European style. Tonni may be in Kentucky, but he is clearly a Dane by training, sensibility, and results. In my opinion, Alex is sui generis and resists classification. From literally tens of hours of talks I've had with him about his approach to design and manufacture, he is probably more influenced by the Scandinavians (particularly Bo Nordh) than by anyone else.
In closing, as I wrote above, I can only claim these as my ruminations and conclusions from a number of interviews, conversations, and attempts to compare and contrast NA work with other work.
I do not - by any means - consider my opinion authoritative.