The only browser you can run on iOS is the Mobile Safari, which is ok. Apple is slowly bringing in WKWebView which will be even better than Mobile Safari (there are still some issues apple has to crack though).
And when it comes to Android devices, AppGyver works with Intel and crosswalk is used to bring unified experience on all devices. Crosswalk is fork of the newest chromium codebase. Check out https://crosswalk-project.org/ for more information about this.
Are you talking about UIWebView (rather than Mobile Safari)? And WKWebView is already available in iOS 8. The biggest thing that WKWebView brings to the table is JIT for JS which previously was available only to Mobile Safari and not to applications using UIWebkit. It does this by running an isolated process pool for rendering web content.
And when it comes to Android devices, AppGyver works with Intel and crosswalk is used to bring unified experience on all devices. Crosswalk is fork of the newest chromium codebase. Check out https://crosswalk-project.org/ for more information about this.