I’d like to begin by saying most people will not notice any significant difference between Webform 8.x-5.x and Webform 6.x because most of the noteworthy changes are happening under the hood to APIs and configuration: there was a bump in the Webform module's road to Drupal 9, which helped fix subclassing and stop the overriding constructors. This change became the initial commit to the Webform module's 6.x branch. Most of the subsequent commits to the Webform 6.x branch addressed the removal of deprecated code plus some minor tweaks to settings and options.
Removing the Webform module's dependency on jQueryUI
The most noticeable change in Drupal 9 and Webform 6.x is most jQuery UI asset libraries are deprecated and moved to contrib modules. The Webform module was using the jQueryUI's Tabs, Tooltip, and Date picker plugins. Although I considered keeping the requirement of these plugins using Drupal's corresponding jQueryUI modules, after some nudging from the Drupal community, I decided to replace the jQueryUI Tabs and Tooltip and make the jQueryUI Date picker an optional dependency.
Below is a screenshot of Tabby in the Webform module's user interface.
Below is a screenshot of Tippy.js's tooltips in the Webform module's user interface.
Some minor tweaks to settings and options
Some minor tweaks were made in Webform 6.x to improve settings, options, behaviors, and features. For example, URL aliases on the Webform module's General setting form are now prefixed with a forward slash. This approach is more consistent with how Drupal core handles URLs/paths.
One of the biggest changes, which does not impact any existing installation of the Webform module, is the Webform module's default 'gender' options are more now inclusive. Personally, I like ensuring that the Webform module user experience reflects the diversity and inclusivity of the Drupal community.
Finally, one major tweak to translations
And the last tweak I want to mention is the one I made to the user interface for translating webform elements. Translators no longer need to use a YAML editor but now instead can edit individual element labels and descriptions.
Tips for upgrading to Webform 6.x
Right now, there is an initial beta release of Webform 6.x for Drupal 8/9. This beta release means that the APIs are frozen. There will be an upgrade path between beta releases. This beta version is intended to give people a chance to help with some testing and quality assurance. There should be a stable release coming very soon.
Besides updating the Webform module using Composer or manually, everyone needs to update the Webform's module external libraries, especially the Progress Tracker, which was upgraded from version 1.x to 2.x. Finally, please make sure to test everything on a staging or local server and confirm that your exported webform configuration is also up-to-date.