Higher security is the main difference. Newer firmware also have some new features but other than install code support non of the other new features are exposed in ZHA or Zigbee2MQTT as of yet.
While you from an end-user experience would not notice it feature-wise, when you form a Zigbee network from scratch using a Zigbee Coordinator with newer Zigbee 3.0 based firmware then it will form a Zigbee 3.0 network and connect Zigbee 3.0 devices using a higher security standard, (older Zigbee devices will still connect but use older security standard, e.i. the highest security they support. e.g. usually Zigbee Home Automation 1.2 or Zigbee Light Link 1.0). This is even more granular since there are several different revisions of Zigbee 3.0 so using latest firmware Zigbee Coordinator should give higher security.
However if you use an Zigbee Coordinator with older Zigbee 1.2 based firmware (like the ConBee II) then all devices connected will be connected using a lower security standard, but as long as a device can be paired/joined then it should still be possible to use all the devices features, hence you not noticing any difference from an end-user experience point of view.
There might also be a few rare Zigbee 3.0 devices on the mark that do not offer any backwards compatibility mode and can thus not be paired/joined at all to an older Zigbee Coordinator but that is extremly unusual.
The point is, if starting from scratch then do not go out and buy an older Zigbee Coordinator adapter, and do not recommend buying an older Zigbee Coordinator adapter to people that do not already own one.