To immediately get into the weeds, both mentioned versions are now capable of running firmware version 2C54. The second-gen AirPods were on 2A364 while AirPods Pro launched with 2B588. It’s the first time both versions have bene updated to run on the same firmware.
Given AirPods are wireless, the update is likely to be focused on improving connectivity with both iPhones and other Bluetooth devices. These two versions also, unlike the first-gen AirPods, have handsfree Siri, which could well have been improved.
The update is unlikely to improve battery life, but we live in hope.
There’s no way to force the update and Apple doesn’t say how to do it. When we checked our AirPods Pro they were already on the new firmware though, so we must have received it at some point. Just keep using your AirPods normally and Apple will push the update to you in due course.
To check, connect your AirPods to your iPhone and then go to Settings > General > About > AirPods (or AirPods Pro) > Firmware Version.