Both of these versions of the widget look similar. They are responsive, and look like the horizontal category tabs you see on your starter site.
All e-shop designer themes will now style the new widgets appropriately for your theme.
Tweak settings for category tabs will also now work for these new widgets. The tweak preview can also be configured to show the original, v1.1 or v2 versions of the horizontal category tabs widget, and the sample widget code will include the appropriate widget code.
You can update you existing theme/tweak to get this support if necessary. See https://eshopdesigner.uservoice.com/knowledgebase/articles/864690-keeping-your-themes-and-tweaks-up-to-date