So, one of the main features of coding using the native SDK provided by
I built a large application within the last year (2013) with different components: mainly an API (ASP.NET Web API => C#), a Website (ASP.NET MVC => C# + AngularJS), and both an app for Android (Xamarin.Android => C#) and iOS (Xamarin.iOS => C#). The decision to use Xamarin had its advantages and its disadvantages, but all in all I am more than happy with it.
That comes especially into play regarding the code sharing aspect: our client applications aren't really thin clients because of some offline functionality which requires a lot of synchronization logic, so the UI part of the two apps is only one side of the medal. As it turned out, I could really use 90% of that non-interface code on both iOS and Android. This is an incredibly huge benefit, as it's not only about some language originalities of Swift/Objective-C or Java, but also about the different frameworks you are using on iOS and Android. To use the .NET Framework/Mono as foundation of every Xamarin app enables you to abstract things like data access or network communication from the underlaying OS.
In terms of speed and UI you don't have any disadvantages, because you're using the native APIs 1:1. Whatever is available on iOS or Android is also available through Xamarin. And whenever Apple for example ships a new version of iOS, Xamarin will ship the update for that within a few days, so you don't have to wait to be able to use newly introduced features by Apple.
Xamarin uses a technique called Ahead of Time Compiling on iOS, so everything you write in C# is compiled into the native iOS stuff before it is deployed to your device. That means there is no difference in what is executed between a "native" Objectice-C application and a Xamarin application (except some small overhead which isn't noteworthy from my experiences).
On Android Just in Time compilation is used as just with any other "native" Android app, too.
That all means you have all the exact same APIs and possibilities you would otherwise have, if you would go with Objective-C or Java. You even use the same objects for building your UI with the exact same types and names (sometimes slightly optimized ;)). So if you want a tab bar navigation for your app - you use a UITabBarController for that. See iOS vs. Xamarin.
After multiple years on my way with Xamarin I only one disadvantage:
Possible memory leaks. Their whole samples out there are a bunch of crap regarding essential basics of preventing memory leaks. If you are working with "expensive resources" like media files within your application, you should take care from day one. I had to get rid of all that problems when an app of mine had already been growing to up to 35 different (complex) dialogs. That took me almost two months or in other words thousands of bucks. They provide some documentation about it, but the tooling is poor at this end. And errors are likely to appear and very hard to be found (example).
But all in all it was one of my best decisions to go with Xamarin.