The XDK builds a webview app (or hybrid app) that runs in a webview on the target platform. That means it runs in a Safari webview on iOS, on an Android webview on Android targets (except for Android 4.4 which uses a Chrome mobile webview), on Windows Phone it's an IE10+ webview, etc. It's essentially the same as a PhoneGap or Cordova app.
One thing that is very unique, for Android 4.x platforms if you build for Crosswalk you'll get a custom webview that is based on Blink and is identical for all Android 4.x systems (sorry it doesn't run on Android 2.x or other targets). Since Android is the toughest webview to work with, the Crosswalk target is really a useful option, it makes life much simpler.
So that means that, yes, you must account for differences in the platforms, but if you can get it working first on Android, the rest are generally limited to dealing with differences. If you use Crosswalk, then Android is easy. After that iOS is probably next easiest. Windows is a mixed bag and is the hardest to debug, due to limited tools for accessing the webview.
p.s. You can look inside the package generated by the build system to see what is in there.