TL; DR
The truth is that, from the point of view of the client App, it makes no difference whatsoever in what technology the Web Service is implemented. This is just the idea of Web Services to get started.
Therefore, the factors that can lead to the decision of which platform or language to use are elsewhere.
Some are ...
Two different environments?
Unless you are already a proficient .Net developer, if you already develop in Java for Android, using the same language on the server makes more sense.
Server cost
Unless it is a personal project funded from your pocket and without a significant return, the cost of hosting should not be a problem.
However, for Java, the initial cost is higher, since a small instance of Java takes up too much memory. The advantage of Java is that the memory is not proportional to the number of users.
In addition, there are services like OpenShift that allow limited use for free.
Other alternatives
On the other hand, if you want to keep a minimal cost or know neither Java nor .NET and want a simpler environment, you could even use PHP or Node.js to develop your Web Services.
Operating system
The operating system is also not important in the sense that both will support.
But in general, the linux environment is more flexible and lightweight. There are distributions made for use in the Cloud that work with little memory and little storage space.
The problem with Linux is that if you are not used to this kind of environment and do not dominate the terminal, you can easily waste a lot of time punching a knife until you can do simple things that Windows could resolve in a few minutes by clicking on some menus.
