Disclaimer: I created Awesomium. Nevertheless, I will practice the utmost objectivity in my response.
Awesomium does cost a bit of money but it is definitely the best tool for the job, I'll defend my reasons with a bulleted list:
Simple, well-documented API; we've tried our best to keep the API as intuitive and readable as possible. That's really important when you're embedded something as large and complex as an entire browser framework. (Believe me, you don't want to embed WebKit directly-- that's like swallowing the sun.)
Windowless rendering; the library was designed from the outset to be used outside of a standard "windowing framework". We make it really easy to render a WebView to a texture:
void update()
{
if(webView->isDirty())
webView->render()->copyTo(texture, width * bpp, bpp, false);
}
Solid Javascript integration; if you use Awesomium as an HTML GUI renderer for your 3D game, you'll definitely want to take advantage of our Javascript <-> C++ integration. You can call Javascript functions directly from C++ and vice-versa, set callbacks, expose global properties, and more. I wrote up a big guide on my blog here.
Well-supported; we use the money we get from our top-tier commercial licenses to fund support and development of the library. If you need help, please visit http://support.awesomium.com and we'll be glad to lend a hand.
The library is free for non-commercial use and very affordable for indie developers. If you'd like to use Awesomium in your next project and are worried about the price-point, please email me at [email protected] and I'll see if I can't help you out. :-)