With an instance of SQL Server regardless of using IaaS or on-premise, you would want to focus on all the waits that are occurring in your instance because the resources are dedicated to you.
In database as a service (DaaS), Microsoft gives you a special DMV that makes troubleshooting performance in Azure easier than any other competitor. This feature is the dm_db_wait_stats DMV. This DMV allows us specifically to get the details behind why our queries are waiting within our database and not the shared environment. Once again it is worth repeating, wait statistics for our database in a shared environment.
Click through for a stored procedure John has provided to collect wait stats in a Waits schema.