I provisioned an instance of Ubuntu 14.04 in Azure to host my River4 Docker container, and it has been running for just over 20 hours with no problems. I am not sure how long I will keep this instance running, I may take it down at any time. Update: I have shutdown the instance and removed the link to it.
There are a couple of things I like about Azure over Amazon. One is that they provide a relatively friendly DNS name for your site. While one can access the River4 home page via a public IP, I think DNS names are much more user friendly and Azure certainly makes that much easier. (Amazon will provide a public DNS but they tend to be really long, and in my opinion, un-friendly.)
The other thing I like about Azure is that they provide a lot of nice, easy to use monitoring tools. In fact, I think the user interface of the Azure portal is much more friendly than Amazon. If you are at all interested in monitoring your River4 instance, I think Azure makes that much easier.
On demand AWS Pricing for a t2.micro instance, which is their smallest, is $0.013 per hour. If you go with a reserved instance for one year, you can get the price down to $0.009 per hour. Azure's on demand pricing for a basic instance, which is their smallest, $0.018 per hour. Azure billing rounds up to the nearest minute, while AWS rounds up to the nearest hour.