Relatively speaking Europe is a lot more Automated than the USA. The US probably has larger warehouses but they are standard warehouses. The trend in the US has been less storage and more conveyor sortation in the warehouses over the last ten years. Instead of keeping your stock on racks, keep less stock and when it comes in sort it and ship it out.
Because Amazon has bought Kiva it has effectively killed it for use by other retailers.Nobody is going to let Amazon know their internal secrets. I think somebody will come out with a Kiva clone shortly