I don't have all of the low-level details, but from a high-level view, the basic difference is that PS/2 is a "stateless" connection, where USB is a "stateful" connection. By that, I mean that the PS/2 controller on the motherboard is always there and takes any input within the expected range. USB is different, though, in that the USB controller is a generic controller and requires a "smart" device to connect, respond to USB query ("polling" is the technical term) events and identify itself as a correct USB device and sort of synchronize itself with device manager.

It's much the same as the older 27Mhz wireless keyboards versus Bluetooth. 27Mhz stuff is generic broadcast, where Bluetooth requires an authenticated connection for every single device.

It should be noted that while this is generally true, there apparently exists a USB hardware broadcaster, it's just notably more expensive than PS/2.