Top to bottom:
Dumbledore would be obsessed with obtaining Golden Galleons, and wouldn't care about the students, but would use those galleons to buy resources for stonger wands and would make them much cheaper for families to buy for their 10 year old boys and girls.
Harry would have the same story line, but he would only seem nerdy because of malnourishment (emotional as well as physical) thanks to living on the streets for most of his life. Otherwise he would have been street smart, but not book smart, leading to him learning Quiddich quickly. This talent of his would have impressed Dumbledore, because having him on the Quiddich team would have let him bring in more galleons.
McGonnogal would have been pretty much as she was in the UK, but a little crankier because she was making only 75% as much as Snape. Dumbledore would half-heartedly complain about this but not do anything about it, because Snape and the Death Eaters were secretly funding his plans to destroy Voldemort, which he had convinced them was impossible.
Hagrid would have hunted him down during a rainstorm on his 10th birthday, while he was hunkered down in a dumpster explained the situation, and flown him to Grand Central Station. There he would meet a family of 5--An African American woman and her four children: Ron, also 10 and attending Murika School of Occultism and Percieved Sham Science; Fred and George, twins who both worked two jobs to supplement the income of their family so their two younger siblings could attend Murika and have a better life, and Ginny, Ron's 8 year old sister whose blue eyes, curly red hair, and fair skin was a pretty clear hint that even before their divorce two years earlier, Ms. Weasley had been being unfaithful for years.
They would have been shocked to learn of him, but the scar would have made it clear that he was the real deal. They would have helped him figure out how to maneuver his cart through gate 8.25, where he would have meant Ron and Hermione.
Ron would have looked like he was described in the books, but would have actualy been a closet genius who hated to share his secret and would have solved many if not most of the mysteries in the books. They would have been forced into the same 4-seat compartment on the Murika Train with Neville, and that would have gone mostly like the original books, except that Ron would have been resentful of Harry and wouldn't accept Harry's offer of free candy, saying that he came from a hard-working family and could take care of himself while eating his bologna and white bread sandwich. At which point, Hermione comes in to take her seat across from ron and next to Harry.
Hermione immediately strikes up a conversation with Ron, who seems like the jocks she wished she was grown-up enough to date back home, and ignores Harry and Neville. Most of the train ride goes the same, except Hermionie is shown to be the shallow cheerleader type that kids around that age are really curious about.
**I've never been to England and I didn't plan to get into detail--just to show some differences between our cultures. If anyone wants to pick up where I left off, I'd be happy and I'll add to it if anyone enjoys it. Just keep it close to real if you don't mind.