I don’t know if it is possible to use FIrefox (or another browser) as an ActiveX control. It might be but I’ve never tried.
The ability to pass a URL to AtlAxWin is something built-in to Windows. I would hope it would use the latest version of IE, but I don’t know how to control that. You might be able to pass a ProgID or CLSID and specify a particular browser version.
One advantage of using a separate browser (instead of BrowserControl) is that users don’t need to run Suneido, they just need a browser. But that is only relevant in a multi-user situation.
I looked at using Chromium Embedded with Suneido but didn’t finish anything. (See my blog post.)