Azure Cosmos DB is Microsoft’s globally distributed database service. The service is intended to allow customers to elastically (and independently) scale throughput and storage across any number of countries.
Azure Cosmos DB is a non-SQL database that gives access to information (JSON) quickly, with high availability, scalable and with global replication.
Microsoft Azure SQL Database as a Service offering with high compatibility to Microsoft SQL Server. That is, a Relational DBMS.
In my opinion, it would be more convenient to use Cosmos DB because you'll be able to access the info (via JSON) without having to create a web service. And it would have limitless scale. One important thing about Azure Cosmos DB is that its collections grow as your app grows. You can start with small data size and throughput of many requests per second.
Instead with Azure Database SQL you would have to create an ASP.Net Web API project to be able to access the data. (This could affect development time).