Map Web SDK's in general will have a lot more capabilities than native map libraries for most map platforms. The main reason for this is that it is significantly easier to develop web SDKs, and most map platforms build new capabilities their first before bringing them to native SDKs.
Native SDK's have the potential to have better performance, however, with the Azure Maps Web SDK using native rendering via WebGL, this is generally not noticeable, and with additional optimizations built into the Web SDK, it actually performs better in many cases.
The main capability that a native SDK that the Azure Maps capability doesn't currently support (atleast without a decent amount of work) is offline maps), although I don't believe the Bing Maps iOS/ Android SDK's support offline maps.
As for Geofences, it depends on the type of geofence you are dealing with. As far as I'm aware, Bing Maps has never provided any Geofencing API for any platform or as a service. iOS and Android themselves have a native geofencing API that you can run in the background, but that is independent of Bing Maps. For example:
If by geofence you mean Polygon, yes Azure Maps does support polygons. If you have polygons for Bing Maps you would need to convert the classes to something Azure Maps equivalent (GeoJSON is generally used), however the actually coordinate data will work just as well in Azure Maps. So, just a data model change, not a data change.
If you are in fact looking for a Geofencing capability beyond what is natively available in mobile SDKs, Azure Mapa also has a geofencing API that is useful for fleet management type applications. You can find a tutorial on this here: https://learn.microsoft.com/en-us/azure/azure-maps/tutorial-iot-hub-maps