As I understand things, if you need to develop a desktop app and stick with Microsoft products, use the .NET SDK. You can also develop native apps for mobile Windows phones; also, for the Windows app store.
This guide might help:
Design considerations—ArcGIS Runtime SDK for .NET | ArcGIS for Developers
Unless you are targeting Windows phone, I would be inclined to recommend the JavaScript API. You can host this within an ASP.NET application, or just use straight HTML5/JavaScript. You can get also develop responsive apps using Bootstrap and ArcGIS. Additionally, keep in mind technologies like PhoneGap - PhoneGap | Home
Write it once and deploy it everywhere!
Esri/quickstart-map-phonegap · GitHub
Depending on who you ask, some will say native apps are killing the web, or the web is killing native apps... pick your poison - no one can predict the future. I was a Silverlight developer 5 years ago; JavaScript was quant. Not so much these days; Silverlight is dead, JavaScript is king. I'm betting you'll get more mileage out of the JavaScript API.
