The real difference is the age of the cities. Cities that grew up before the age of the automobile usually have good public transportation and are dense (because they had to be). Cities that grew up in the age of the automobile, especially in the US after the war, have prolific sprawl and little investment was made in planning for public transportation, because it was not needed. Again, with travel between cities, if the cities existed before the age of the auto, then there are rail lines with passenger service between them; otherwise, it's hit or miss.

Obviously, the average age of cities in the UK is older than those in US...