As for the single tab hiding, that could become an issue if there were two tabbed documents and one was dragged underneath the other. Then suddenly neither would have a tab visible, since the tab hiding is based on the number of visible windows is each container.
It does look like the Browser UI sample isn't using those properties correctly. I think at some point we added related properties on TabbedMdiContainer itself and those get bound down to set the AdvancedTabControl in the TabbedMdiContainer template. Thus setting those properties on AdvancedTabControl's Style won't do any good. They need to be set on an implicit TabbedMdiContainer Style instead. We'll fix that sample in the next build.
If you add this implicit Style in your Application.Resources, it will make constant document tab widths:
<Setter Property="MinTabExtent" Value="200" />
<Setter Property="MaxTabExtent" Value="200" />