With AWS on its own you dont get the one click deployment process or the management dashboards that Mendix provides. You also have to add your own monitoring and manage your hardware. Mendix are in the process of making the mendix cloud available on AWS with Cloud Foundry PaaS on top. The free apps already run on top of AWS.
I had same question recently, it depends as I have seen the most on these things:
1 - cost; minimum cost to launch at AWS (Azure) is higher then on Mendix Cloud
2 - flexibility: AWS has more flexibility when you want to scale up in hardware
3 - control: in AWS you can control more then in Mendix cloud
details see AWS
I think that when flexibility and control becomes more important than price, AWS would be a better choice.