The browser shipped with Blackberry 10 was written in HTML and was a real joy to develop.
Edit: some more public details
The default browser on the BlackBerry 10 platform was a completely new browser application. The chrome was written in HTML, CSS and JavaScript. Being able to develop the chrome on your desktop browser or being able to run inspector remotely and using your desktop was very handy. The core was a command line application called webplatform that "launched" a url that was a "webapp". The webapp had API's exposed to it such as creating WebView's in or out of process (yup blackberry has had multi-process tabs for a while now...). One joy was being able to pull up the Javascript console for the browser WebView and dynamically calling exposed c++ API's in any WebView in any process to test out features or diagnose problems.
It started out as a quick little proof of concept I tossed together over a day and the upside was large enough to invest time into. One of the reasons for making the main browser in html was that as a platform we wanted web application to succeed. Eating our own dogfood we made sure webapps could handle the job. The API's that were needed were there, memory usage were low, startup time was fast etc. And if you search for reviews of the blackberry 10 browser you will find that the end result was a success.
Edit 2: Much more in depth information can be found on this video which was a presentation given at Blackberry Jam by several of my colleagues. Skip to the 23 minute mark to see some actual code of what a webapp browser would look like.
Another very cool feature I forgot about was that when developing the browser application on the device it would not actually have any browser bits on the device, but just have the environment variable CHROME_URL set to my desktop where I had a webserver serving up my browser files. This let me very rapidly develop the html/css/javascript code without having to transfer my "mobile app" to the device. Reducing the edit/"compile"/see cycle was a big win.
I left RIM in 2012 so I could not confirm that this is how the browser works in new devices released today. But given the success and advantages that having the html browser gave us there would have to be some really compelling reason (or $$$) to abandon it. The group I was part of was formally TorchMobile and as a group had significant browser experience having written a fair number so we understood the hassles of maintaining two projects. Being able have webkit developers help with part of the browser made development go faster on both sides (webkit devs could easily abuse the browser to test new feature). Even if it isn't used in the browser as mentioned at the bbjam the weblauncher application was used by not only the browser, but for a number of other purposes.
I can only imagine there is a fair amount of overlap in Mozilla where there are two developers working on the same thing, one for xul, one for html.
Edit: some more public details
The default browser on the BlackBerry 10 platform was a completely new browser application. The chrome was written in HTML, CSS and JavaScript. Being able to develop the chrome on your desktop browser or being able to run inspector remotely and using your desktop was very handy. The core was a command line application called webplatform that "launched" a url that was a "webapp". The webapp had API's exposed to it such as creating WebView's in or out of process (yup blackberry has had multi-process tabs for a while now...). One joy was being able to pull up the Javascript console for the browser WebView and dynamically calling exposed c++ API's in any WebView in any process to test out features or diagnose problems.
It started out as a quick little proof of concept I tossed together over a day and the upside was large enough to invest time into. One of the reasons for making the main browser in html was that as a platform we wanted web application to succeed. Eating our own dogfood we made sure webapps could handle the job. The API's that were needed were there, memory usage were low, startup time was fast etc. And if you search for reviews of the blackberry 10 browser you will find that the end result was a success.
Edit 2: Much more in depth information can be found on this video which was a presentation given at Blackberry Jam by several of my colleagues. Skip to the 23 minute mark to see some actual code of what a webapp browser would look like.
https://www.youtube.com/watch?v=bZ8vxhTezvs