On desktop platforms, using the system's control styling, etc. is a very common practice and changing it ("theming") is usually looked down upon unless the application specifically calls for it (like a themable music player).
However, on mobile platforms (smartphones), I've noticed that this isn't all that common. Many apps prefer to throw the platform styling out of the window and simply use their own. Also, apps that use their own styling appear to be "better" than those that use the system styling. (I'm talking about Android apps in specific, and about my own opinion.)
So, my question is, what should one do in such a situation?
EDIT: Native app.