I do not have any specific data but have heard that some people have said that the Postgres Aurora promising performance. When it comes to performance, there are MANY different factors involved.
Please note that Aurora is supported starting at ArcGIS 10.7.x and not tested on versions before that. I would recommend using it with ArcGIS 10.7.1 or ArcGIS Pro 2.4.3 for the best compatibility and performance.
I would also not recommend using SDEBINARY if at all possible as newer tools and functionality may not work correctly.
Are you accessing the data from a local (in office machine) to the DB in AWS?
--- George T.