App service is a more managed service , SF is more you manage your own and you can run on your own premises as well. SF has better support for non MS stack dev eg native apps etc.
As that document states "Service Fabric is a good choice if you’re creating a new app or re-writing an existing app to use a microservice architecture. "
If your hosting a few apps you should not be looking at SF , On the other hand if your deploying more than 10 services than it becomes a better solution.
Also note SF has a data storage mechanism that is included with the services . It is good at 3 things
1) Massive clusters of data
2) Simple data, often in Micros services DBs become a heavy burden since each service should have its own data and things like SQL are bit overkill when you only have 1-3 tables.
3) State storage for the Actor programming model.
I think SF and Web apps will slice the "Cloud Service" user base in the future.
