HockeyApp replacing App Insights...definitely not...
In Summary: App Insights originally shipped with a set of SDKs for mobile platforms that pushed telemetry data into the App Insights pipeline. It is these SDKs that are being deprecated in favor of the HockeyApp SDK, not all of App Insights.
Hearing from the community, with the introduction of HockeyApp, there is some confusion on the roadmap for gathering telemetry data from your various applications.
First, HockeyApp does NOT replace App Insights. It compliments App Insights for mobile applications. App Insights is the strategic direction for Microsoft as a whole. HockeyApp is a nice compliment to the solution and brings exciting DevOps features to the Mobile Apps platform such as beta distribution, crash reporting and user metrics. It's widely used for mobile apps across the industry and delivers everything in the mobile space for many folks.
App Insights gives a unified view of all of your telemetry data. A solution may consist of a mobile app, web services, databases, and other components that also emit telemetry data to be collected and analyzed. This is where App Insights brings together that unified view of your telemetry data.
App Insights originally shipped with a set of SDKs for mobile platforms that pushed telemetry data into the App Insights pipeline. It is these SDKs that are being deprecated in favor of the HockeyApp SDK, not all of App Insights.
Telemetry data collected from this HockeyApp SDK is sent to the same telemetry processing pipeline that App Insights uses, but at this time only shows up in the HockeyApp portal, not within the App Insights Portal and associated features like Continuous Export and Application Analytics. This means that you have two places to go for insight and don’t benefit from a unified view of telemetry across your architecture when you have a solution made up of Mobile Apps and supporting services.
The good news is that this will be fixed in the near future and is a relatively straight forward change due to the use of a shared pipeline.
There is a significant commitment to invest and deliver more with Application Insights, some great recent examples are: Application Analytics (based on Kusto), Proactive Detection, Application Map and Live Stream Metrics.
In summary, please use HockeyApp for your mobile application and WPF/Desktop telemetry needs and Application Insights for everything else. The overall proposition is now stronger with HockeyApp and Application Insights coming together.
Whew, hope that helps clear it up. =)