An app built with React Native is indistinguishable from a "real" native app, unlike cordova apps it doesn't run in the browser (or in a webview).
For example, I believe that both the navigator components for React Native in iOS currently suffer from either bugs or performance issues. The more native one has an open issue related to UI flicker, and the JavaScript-based one drops frames when subviews are complex.
That statement might not be true tomorrow or next week, because the ecosystem is developing quickly. Generally I am very happy with React Native.