I have a 14 and 12 year old (11 and 9 when we moved over).
Kids are resilient but there is still a period of adjustment. As parents, we always framed the move as a big adventure. Our kids are free spirits anyway, so they embraced the idea of an adventure.
Having said that... mine struggled for the first month or so at school. As much as our Aussie education system is lauded, there was ALOT of basic stuff they had not been taught in Oz that was expected knowledge in the US, and they had a small crisis of confidence that they were dumb. But they caught up pretty quickly. Our oldest was able to complete sixth grade in just four months AND win a President's award.
Retaining their identity as Aussies was important to both my kids. They still watch AFL and Union. We make our own food (meat pies, lamingtons, mars bar slices) to keep the connection to home. Especially in those first few weeks, comforts from home are super important.
There are words Americans used that my kids didn't understand at first. I remember my little one coming home in the first week of school saying 'I keep on getting into trouble, mum. My teacher says 'hush' and I don't know what that means'. 'Hush' wasn't a word he'd heard before so he would talk to his classmates, his teacher would tell him to 'hush' and he would keep on talking because he didn't understand the instruction. Lol.
Making friends for my boys was pretty easy. The accent is/was a superpower (especially in the south where we are). And kids are the same the world over. Within weeks, my boys had established friendship groups / connections that they maintain to this day.
Short story: prepare for an adjustment, prepare for a few tears, and prepare for them to go through an experience that will be the making of them. Moving to the US has changed my boys for the better in so many ways.