I'm American and my husband is English.
I have brought up my three children in both England and the US. They are currently 30, 24 and 21.
Many of the expats that I've encountered, in either direction, have emigrated due to their jobs with executive perks. That was not us. We emigrated for marriage. My husband was a telecoms engineer when I moved to England and he's currently a small business owner and a professional photographer here in the US. In other words we have regular jobs with a decent income so our situation is different from many other people. No executive perks for us.
I liked living in England and I enjoyed that my children had a decent education and a very good standard of living. I did have a few troubles though because I am a dark-skinned Mexican-American and I did encounter difficulties in the workplace due to my skin color. I let it go but my oldest son did have a difficult time with ethnic slurs and straight-up discrimination. They were handled but it wasn't pleasant. It turned me off of living in England, a little bit, if truth be told.
My oldest and second child did experience culture shock when they moved over to the US. They didn't quite feel as though they belong and only recently, feel American. They're always within three cultures (US/Mexican/UK). I live in an area with a large international immigrant community, which has been accepting but it's the English expats that have made them feel shit and say ugly/ discriminatory comments because again, they don't "look" English or speak like English children. We have not been approved for UK expat groups because of this. That has been a weird eye-opening experience. It would probably not happen with you, OP.
My youngest child was four when we came and she's had a full US experience. It's been good here and it's been positive. All three have gone to good schools, been happy, had good friends. Overall, my husband and I have felt okay about raising our children here.
I will say that it's hard for me to give advice to you though because we raised our children in a different time. We lived in England during Columbine and 9/11. My country changed overnight. I didn't grow up with shooter drills (I was born in 1970). That didn't happen at my children's schools until recently. I have school-aged grandchildren and they have a different experience than their father had. To be honest, even the idyllic English life we had doesn't really exist anymore either.