According to Visonic there is a very big difference between the two models as they use different protocols.
There’s no mystery about it. SmartThings uses the zigbee home automation profile (ZHA1.2). Devices that use that protocol can usually be controlled by SmartThings. Devices that do not use that protocol, even if they are using zigbee, usually cannot. Some devices using other zigbee profiles will be able to be paired with SmartThings, but they will not be able to be controlled or they will repeatedly lose connection.
The 340 uses the same protocol as SmartThings.
The 320 is made on a number of different frequencies, but I don’t believe any of them are using ZHA 1.2.
Check the user guide for your particular model and see what frequency and profile it is using.