Ionic Framework let you make hybrid mobile Apps with AngularJS, while Xamarin allows you to make Native apps for Android, iOS and Windows using C#
My opinion goes to xamarin, It's a right one to create cross platform applications, recently I done my mobile app project with one of the xamarin app development solution here. contus.com/xamarin-application-development.php Yet I'm not get any problem with the app. Also you can find some advanced functionalities in xamarin. It's really good to go with xamarin for creating app in multiple operating systems
Ionic is a framework for developing hybrid mobile apps in HTML5 and AngularJS while Xamarin is a framework for develop native apps for iOS, Android and Mac in C#.
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5 Points Comparison On Hybrid Technologies – React Native, Xamarin And Ionic Framework, Please visit here: goo.gl/bY46j0