Smart Home Controllers with local processing don’t depend on the internet, so your hardware needs to be of a high standard to run your devices, logic and scenes.
On the other hand, some Controllers run their functionality via the internet, hosted on the manufacturers cloud service. This allows them to centralise their infrastructure and tightly control security, features and functionality all in one location.
Cloud-based Controllers are often cheaper because they run the bulk of the system remotely, and as you expand your system, the service scales-up to accommodate additional devices.