Somehow I had the feeling that I was in control when it came to specifying the browser I wanted to open.
Apparently, it’s true for external browsers. For internal browsers, ie those that show in a view or an editor in Eclipse, not so much.
What happens is that the information get lost. You specify the browser type when you do the call to open the browser:
PlatformUI.getWorkbench().getBrowserSupport().createBrowser(SWT.MOZILLA, ...);
But this is simply ignored by the internal editor. Not for too long though, since I attached a patch to 259171 fixes the problem.
Your feedback on this is welcome, of course please feel free to comment on the bug rather than here.