The most important change in this release is compatibility with Ubercart 6.x-2.10, see #1697988: Cluttered admin screen with Ubercart 6.x-2.x-dev from July 18, 2012 or later. All other changes since 6.x-2.0-beta2 are quite minor (such as fixes in automated tests) and you probably will not notice the difference when updating from that version.
When to update
Users of 6.x-2.0-beta2 don't need to make haste with updating, unless they also want to update Ubercart to 6.x-2.10 or later.
Users of 6.x-2.0-beta1 are encouraged to update, since a lot of bugs introduced in that version have been fixed since then.
Users still on 6.x-2.0-alpha1 should be careful when updating, as Extra Fields Pane's API had changed significantly between 6.x-2.0-alpha1 and 6.x-2.0-beta1. Read UPGRADE.txt for more information.
Changes since 6.x-2.0-beta2
Bug fixes
Issue #1659486 by MegaChriz: fixed bug of UCXF_Value's db_name being empty which could result into a UcAddressesInvalidFieldException error when the UCXF_Value was "loaded" just after it was saved in the same request.
Other changes
Issue #1670052 by MegaChriz: removed functions that were deprecated since v6.x-2.0-beta1.
The biggest change in this release compared to 6.x-2.0-alpha1 is the addition of automated tests. Furthermore, basic Views integration is added. This means that now an address View can be created using fields. More Views integration is planned for a future release, see #1391216: Views integration for the 6.x-2.x and 7.x-1.x version for details. An example module is added to demonstrate a way to add extra address fields using the field handler API, though I recommend using Extra Fields Pane if you just want to add some simple extra address fields (such a text field or a select field).
Just as the 6.x-2.0-alpha1 version, this release includes all "required" features for the module and so it should work properly at least in a basic setup with standard configuration.
Changes since 6.x-2.0-alpha1
Bug fixes
Issue #1381120 by MegaChriz: fixed foreach warning in address book when user has no addresses.
Issue #1412060 by MegaChriz: renamed permissions that contained an apostrophe: "everyone's" has been replaced by "all".
Issue #1668666 by miccelito, MegaChriz: make default addresses on address book page better themable.