One interesting city to contrast the differences is Edinburgh, Scotland. The city was established by royal charter in the early 12th century, so it has been around a while, and a lot of the older parts are as you'd expect.
The part which we now call "New Town" was built in stages between 1767 and around 1850 and has an explicit "block-based" design.
> At one point there was nothing where every single city now stands. Everywhere it started with a blank slate.
Before the city there was a town, or a village. It's not blank slate > city, it's blank slate > something > something else > city. There's some evolution in the middle and that makes the difference. One grows organically over time and goes through different stages until it reaches the "city" stage, one is planned as a city from the start.
The key isn't planning, the key is population. A city without people is a ghost city. The city is as much the people as it is the infrastructure. Cities are alive.
It's like arguing that you can build a person by assembling organs in the right place. You can build a humanoid structure which mimics the human, but it's missing the most important feature: life. You can't simply instil life into something. It needs nurturing.
The difference is the speed of development and, even more importantly, the level of planning.
US cities grew quickly and were planned.
Some modern cities that grew very quickly recently are nevertheless messy because they grew without any sort of planning.
Some cities are quite old but nevertheless follow a grid because that's the way they were planned. E.g. Beijing.
Planning is the key.