The main difference is convenience. The more effort you put into it the more (advanced) features you get.
CocoHue takes full advantage of the Hue's second version of their API, which gives users more features than any other integration available.
The current built-in in integration is using the original Hue API version (doesn't have advanced features, and relies on period polling to update the state of the Hue devices).
The Matter integration via Hue Matter bridge functionality that was enabled in the 2.3.9.192 update is the most convenient way to connect Hue devices, seamlessly, without installing additional apps or custom code. While the Matter bridge gives users less features than CocoHue, it updates the status of the Hue devices instantly, for better home automation experience.
