It seems there is lot of overlap between features provided by both of these services: contextually-aware smart push notifications in-app messaging across all connected devices.
Should we prefer Mobile Engagement over Mobile Servies?
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It depends on what features you want. Also, don't forget Azure Mobile Apps - an extension to Azure Web Apps (Azure App Service) that has the same mobile properties as Azure Mobile Services, but with App Service advantages.
If your needs are more in-line with enterprise usage - you need data access to on-prem or cloud SQL services, offline sync, enterprise authentication, continuous deployment, A/B testing, an associated web site that uses the same backend - then Azure Mobile Apps (Web Apps) is the right choice.
If your needs are more in the consumer / brand space - engagement analytics and in-app messaging, then Azure Mobile Engagement is the right choice.
Both have application usage statistics and push notifications.
One does not preclude the other. You could, for example, write the mobile backend and associated web site in Azure Mobile Apps and then bring in the rich engagement analytics that Mobile Engagement to your apps.
