Both devices bridge KNX devices to smart assistants, but 1Home Server does this using Matter smart home protocol.
1Home Server runs completely locally (except for the KNX ETS auto-detection feature) and is built to run without the cloud. 1Home Bridge still depends on the 1Home cloud to some extent, mostly due to the requirements of the older proprietary assistant integrations.
The 1Home Server also comes with powerful in-house designed hardware and with greater performance to which we have added more demanding functionality such as 1Home Automations.