There ARE some breeders in the U.S. producing good dogs, but they're doing it with European imports as their breeding stock, so I'll leave it up to you if that counts as an American or European GSD.
There are some SUBSTANTIAL differences between US and Eu dogs, and the guys involved in the overseas selection can hit them better than I can, but to simplify things:
American dogs have largely been bred for pets or show dogs. The US has actually altered the physical composition of the GSD to where it's essentially now a sub-breed of the real thing. The most noticeable difference is the dog's topline (the line of it's back and haunches). The US dogs tend to have the "show hip" or "roach back" where their back slants from the front shoulder noticeably downward to the rear resulting in the dog looking like it's almost squatting when it stands upright. This was fucking criminal on the part of US breeders, but it's apparently what the AKC wants to see in a show dog (IDK, I have no fucking use for the AKC). American breeders have traditionally paid VERY little to NO attention to the dog's drives of suitability for WORK. They just bred dogs that looked a certain way.
The black and tan saddle that Americans associate with what a "German Shepherd looks like" is another pretty good indication of what's been done to the breed. The sable coat is the dominant gene in the GSD, all other coat variations are recessive or the result of a masking gene (the whites have a masking gene that blocks coat pigment). The fact that most Americans have either never seen a sable GSD, or at least don't recognize a sable dog as a GSD should tell you a bunch. If you've never SEEN the DOMINANT trait in an animal, then WTF does that say about the breeding process. Again, looks over performance.
There's some other areas such as head size, torso proportion, overall body size that differ. In short, the American pet and show breeders took a working dog and bred all of that out it at the expense of the dog's utility and athleticism.
The Europeans draw a line between show breeding and work breeding. The dogs from working lines retain the straighter back (makes it easy to spot the dogs from Eu lines a lot of the time) and their breeding is centered around the drives and temperament of the dogs they produce for the suitability of for WORK. As I mentioned, there are some body dimension differences as well. The Europeans (reputable ones at least) do NOT breed dogs with hip/elbow issues as these are genetic traits passed on to puppies. Substandard dogs are rated as such and either destroyed or used as pets, but they aren't granted breeding privileges (Toebuster, Kenny, Emouse, someone correct me on that please?).
EVERY single American knows someone with a dog with hip dysplasia, every single one of us is familiar with it. Here's the shit of that: we could essentially ELIMINATE hip dysplasia in the U.S. (in pure breds) within 20 yrs or less simply by requiring an OFA of the parents prior to allowing the breeding to take place. Hip dysplasia is genetic, it's preventable, but US breeders either can't recoup the money involved in screening the parents or just don't give a fuck because the dog and it's owner are long gone by the time the problem arrives and the breeder has cashed his check. The kennels in Eu make their money by being known as producing solid working dogs. The financial incentive is there to produce quality dogs because if they don't they lose business to a competitor with proven healthy dogs.
SO, if you're looking at spending a good bit of money on a dog that needs to WORK for a good portion of it's life, do you take your chances with what MAY be an OKAY line from American dogs, or do you go to the source, where the SV more tightly controls who can breed with what and sets an actual meaningful standard for the dogs?
ETA: I tried to attach some pics of the differences, but it was too much of a PITA, so here's a link that shows some pics of show vs working line dogs, the physical differences are very clear once you see them side by side. You'll never look at a US GSD the same way again after seeing the "Real GSDs".
http://www.pedigreedatabase.com/for...traight-back-gsd-and-roach-back-dog-look-like