I would say MySQL in either Aurora or MariaDB form come close however, Azure SQL Database has a more streamlined approach to delivering a consistent programmability model, supported drivers and feature set.
Azure SQL Database T-SQL is advantageous and more complete than SQL found in Amazon Aurora.
What I came to observe is that a developer becomes more productive and simply gets there faster on Azure SQL Database. The existing development tools remain, no training and tinkering necessary. Whilst some features as say database diagrams are not provided seldom it is a deal breaker.
With MySQL and Maria ETL becomes a bit harder, choices go down in what tools can be used and the pricing typically is not attractive.
Lastly, in my case, some existing off the shelf applications would not support MySQL derivatives.
Being able to manage our databases in the cloud, scale quickly, and only require access to VMs made choosing Azure a no-brainer over a traditional SQL Server installation/integration. We don't have the budget or resources to integrate and maintain servers on our own, so using Azure SQL allows us to manage within those constraints.
We moved away from Oracle and NoSQL because we had been so reliant on them for the last 25 years, the pricing was too much and we were looking for a way to cut the cord. Snowflake is just too up in the air, feels like it is soon to be just another line item to add to your Azure subscription. Azure was just priced right, easy to migrate to and plenty of resources to hire to support/maintain it. Very easy to learn, too.
Azure owned by Microsoft who owned SQL Server, so provided a variety of tools for easy migration/transition and from on-premises to the cloud; and management. I recommend using Azure for any on-prem SQL server databases.
Azure SQL is a clear upgrade to SQL Server 2012 and pretty much has the advantage with all the extra features that it has. Security, queries, exporting tables, T-SQL has all improved. Transitioning 18+ years of an in-house database to the cloud was a struggle, but for the long-term solution it is worth it.
Amazon Relational Database Service is the other obvious competitor. We were already in Azure, so it's not a serious contender for our business due to that bias already, but I do personally find the marketing and documentation of RDS more intimidating to sort through.
It's more easy to shift and get all the services up in no time, provide best up time and monitoring easily so you can get the best services which take care of themselves. It's a better fitting for a large company size.
Comparing with Amazon Aurora: Azure SQL DB is 100% compatible with SQL Server and Aurora is compatible with MySQL and PostGreSQL. Because of if, SQL DB suits large enterprises with hundreds of databases better. Comparing with Oracle: the main issue is that Oracle will try to push all other services available in their product offering.
It stacks up in different ways, for the most part, I think Microsoft is doing a really good job versus the competition. They basically started database type products from the beginning. I've always been excited about updates and can see their progress over time. Get's me really excited when I see new updates.
As we were early adopters with Azure and landed on the Azure PaaS (Platform as a Service), it made sense to use databases that were on the same platform as the application to save on costs. Also, we were impressed with the simplicity of Azure SQL. From a management perspective and an automation perspective it's much easier to have all the eggs in one basket (as long as you plan for the unexpected/disaster recovery).