Xamarin is much closer to native. In particular, unless you choose to use Xamarin Forms, you'll be using each platform's native UI APIs, so your UI will be indistinguishable from an app written in the platform's native language. Also, whereas React Native for iOS is restricted to using the JavaScriptCore interpreter (not even the JIT compiler), the Xamarin toolchain AOT-compiles .NET IL to native code.
Good lord that blog makes for tedious reading! It is like he is on a one man crusade to overturn decades of irreversible missteps with the practice of OOP. Rather than trying to fix an unfixable wrong the author should simply get on board the Actor-based Programming bandwagon instead which is almost entirely aligned to Alan Kay's original thoughts. Being "hung up" on ideologies, especially those which are decades old, is not a good personal development strategy.
You may be right, but I still consider him an authority on developing native apps for Apple platforms, because he has so much experience in that area. So in that context, the blog post on React Native is relevant.
http://blog.metaobject.com/2015/04/reactnative-isn.html
Xamarin is much closer to native. In particular, unless you choose to use Xamarin Forms, you'll be using each platform's native UI APIs, so your UI will be indistinguishable from an app written in the platform's native language. Also, whereas React Native for iOS is restricted to using the JavaScriptCore interpreter (not even the JIT compiler), the Xamarin toolchain AOT-compiles .NET IL to native code.