Which services are behind?
The only one that I've had come up is RDS. Azure SQL is great if your application supports SQL 2016, but if it's mysql/etc you have to spin up your own linux server and run mysql on it (Azure DOES have a template for that at least) whereas on AWS it's a pure PaaS offering.
The cost calculator on AWS is years ahead of the Azure one, but that's not a day by day use thing.
Azure's CDN capabilities are more flexible than AWS, and I'd argue HDInsight is better than EMR.
AWS kinesis beats Azure's event hubs right now.
The inbuilt user management is much easier in AWS, being PKI based instead of Azure AD based.
There's other pieces I've missed I'm sure, hence wondering what services you've used in AWS which are lacking in Azure?