I'm the author of GwtBootstrap3. Before I started to work on GwtBootstrap3 I've been using GWT-Bootstrap, fixed some bugs and added some features. When Bootstrap 3 was released I decided to create a new project from scratch because lots has changed between Bootstrap 2 and 3. Some components were removed while new ones were added, CSS classes have changed etc. Also BS3's primary focus was "mobile first". Regarding GWT-Bootstrap this means lots of refactoring. A GWT-Bootstrap version based on BS3 would definitively not be backwards-compatible. I'm not sure how far GWT-Bootstrap's migration is, see issue #448.
While not all features have yet been implemented in GwtBootstrap3 and some issues need to be sorted out, I would say that GwtBootstrap3 is ready for use in new projects. Some real life projects were already implemented using GwtBootstrap3. A migration from GWT-Bootstrap might be possible but since we didn't intend to be GWT-Bootstrap compatible refactoring is certainly required.
When designing GwtBootstrap3 we took great care to outsource any third party components into an extra module. In this module you'll find useful widgets that are not part of the core BS3 distribution. Unfortunately GWT-Bootstrap mixes core and third party components into one library which imho makes it unnecessarily complex and hard to maintain.
If you're happy with BS2 then you should stick with GWT-Bootstrap.
If you want to use BS3 your only options seems to be GwtBootstrap3 at the moment.