There has been some debate around this point of contention, but even in the most recent documents android suggests that it's not such a good idea to use enums in an android application. The reason why is because they use up more memory than a static constants variable. Here is a document from a page of 2014 that advises against the use of enums in an android application. http://developer.android.com/training/articles/memory.html#Overhead
I quote:
Be aware of memory overhead
Be knowledgeable about the cost and overhead of the language and libraries you are using, and keep this information in mind when you design your app, from start to finish. Often, things on the surface that look innocuous may in fact have a large amount of overhead. Examples include:
Enums often require more than twice as much memory as static constants. You should strictly avoid using enums on Android.
Every class in Java (including anonymous inner classes) uses about 500 bytes of code.
Every class instance has 12-16 bytes of RAM overhead.
Putting a single entry into a HashMap requires the allocation of an additional entry object that takes 32 bytes (see the previous section about optimized data containers).
A few bytes here and there quickly add up—app designs that are class- or object-heavy will suffer from this overhead. That can leave you in the difficult position of looking at a heap analysis and realizing your problem is a lot of small objects using up your RAM.
There has been some places where they say that these tips are outdated and no longer valuable, but the reason they keep repeating it, must be there is some truth to it. Writing an android application is something you should keep as lightweight as possible for a smooth user experience. And every little inch of performance counts!