I'm no expert at either but have worked with both. I'm going to assume that by, "Postgres on AWS" you are talking about Redshift.

My experience has been that a beefy AWS Redshift instance performs significantly better on huge datasets than any comparable Microsoft solution. Many of my colleagues (BI Developers and Architects) would tell you the same. If you have worked on predominately Microsoft products, however, you will find the AWS web interface to be clunky and unpleasant. It took me nearly all day once to figure out how to move a small data set from an S3 repository into a Redshift data warehouse.