I'm Russian, and I brought my 9 (now 11) year old daughter to the US. This process was (and somewhat still is) pretty painful for everybody, especially my wife. Russian women are often called 'sitting hens' back home because of their extreme hyper/over/megacare about all things, especially children. And the whole system is built around this - teachers don't talk to kids, they talk to parents (usually mothers), kids opinions are quickly dismissed just because they're kids "I don't care what you think, tell me what your mother says". Kids adopt to this (they're kids) and sit idle waiting for next command from the upper management. But at the end it turned out to be much easier for the daughter than to my wife. She felt like she suddenly lost control of her child - "what if she gets under the bus?!?!11 what if the will fall from the tree?!! what if she will drawn in the pool?!11", etc. My daughter adopted quickly (again, she's the kid) but in a funny fashion - she's very independent in the school and in the company of her classmates, but still very dependent at home (because it's much easier to manipulate your mother to iron your shirt than to do it yourself, you know).
I can't say that American kids are specifically spoiled. There's fierce competition, who's cool and who's not. In their school it is cool to be cool AND also get into the advanced math class. Pretty tough objective, I'd say :-) Back home (we went to a very good school too) the relations between kids were much more relaxed, but there was much more physical abuse. All cultures have their benefits and drawbacks, but overall I like it here better. In particular because it's cool to be in the advanced math class :-) And because she was very disappointed to learn that there would be no advanced computer class in 6th grade. And because she wants to go to the summer camp in Stanford to learn special effects in video, etc.
But I live in a pretty upscale neighbourhood, one of the best school districts in California, blah-blah. That's definitely offsets perspective.
«very independent in the school and in the company of her classmates, but still very dependent at home» seems to be very typical of young people here in Russia, good point.