The Director's Cut (DLC 6) content is further refined in this version, featuring: Ava’s Murder Mysteries
The "v20210624" version corresponds to the release that brought several long-awaited features: Crossplay Arrival : Enabled cross-platform play for players on Xbox One, Xbox Series X|S , PC (Steam & Epic Games Store), Mac, and Stadia. Max Level Increase : The character level cap was raised to borderlands 3 directors cut update v20210624codex
If you're looking for a more academic approach or a "paper" in a digital library: The Director's Cut (DLC 6) content is further
Which of those should I do next?