Mine moved from UK state primary to an American international school. (DD1 is now in 1st year of middle school/secondary.)
What we were told:
"They'll be at least a year behind."
"They will only learn American history."
The reality:
Both had a bit of catching up to do. DD2, who was in Yr4/3rd grade was expected to have learned all of her times tables up to 12 x, whereas in the UK she was still fannying about with her 6x and 7x. She was given a month to catch up, which she did.
They teach them to think for themselves and analyse early. DD1's exam at the end of Yr 6/5th grade was a corker. She was given a page of A4 text on Sparta, plus a map and was asked to "exlain how Sparta's political and physical geography played a key role in its military victories." Which threw her!
DD2 is studying ancient Egypt in history. Last year she did North American tribes. DD1 is studying mediaeval Europe. Last year was (I think) French revolution and WW2 in Europe.
The breadth of the curriculum (in this school, anyway) is much broader than UK. Last term DD1, with three friends, wrote a short play, acted it out and filmed it, in her arts class. DD1 is learning digital composing and has had one of her compositions entered in a worldwide competition.
Big emphasis on sports, too.