I don't have kids yet, but I'm an immigrant from the US. I have to say I don't fully understand how the school system works here and I worry that I won't be able to provide enough guidance and help navigate things for my future DC when the time comes.
For example, GSCEs and A-Levels and applying for university - it's all a bit of a mystery to me and my DH didn't attend uni so he wouldn't know how to help either. The US system is very different, we take a standardised exam (the SAT) in the final year of high school, and universities use that score along with your grades and any extracurriculars to decide whether or not to admit you.
The school run also seems to be a huge thing in the UK and is apparently a source of drama going by what I read on MN, whereas I used to just get picked up and dropped off by the school bus at the end of my parent's driveway. When I was small (5-9 years old) and lived nearer to the school, I walked there with my friends, but seems like that would never happen here.
Parenting culture here seems more protective and almost over-involved, at least amongst the parents I know (middle class, high-earners). The kids' lives all seem very scheduled and regimented and playdates are a bit formal compared to what I'm familiar with in the US. A lot of fussing about where to live to get the kids into certain schools, when all the schools in that town are good.
It also seems like children in the US receive more medical monitoring, as kids have annual visits to their paediatrician to check their development etc, but here it seems like kids don't see the doctor unless something is wrong and then it's the GP that sees them.
I am a bit worried about pregnancy here, as you see a lot of horror stories and scandals about births gone wrong on the NHS (obv could happen anywhere but it's in the media often). I have some medical conditions where I would be closely monitored by and obstetrician in the US, but in the UK it seems like it's more hands-off and you are typically seen by a midwife. Epidurals also don't seem to be favoured in the UK, and only gas and air/natural birth seem to be idealised (at least amongst the people I know). I worry I'll have to fight to have a consultant-led pregnancy.
I think there are more career progression opportunities in the US (my career has taken a definite hit moving here, and the pay is a lot lower), but my kids would have dual citizenship and could move there if they wished to.