Typically except apps like games are the only ones who have been using full-screen mode, primarily because they want to provide an immersive experience to the user without bothering about other tasks. Also because typically games are heavy on resources and often switching to other apps make the game load all over again.
Also, the intent of user in such cases are only present app and they are less likely to switch between apps.
But in other cases, user do several things - 1) switch between apps, 2) look at date, time etc., 3) at times change their settings and services like brightness, wifi, data, nfc etc.
So it makes sense to have the system bar available to users without forcing them to move out of your app.
There have been cases on Android where some apps are taking a mixed approach. For instance, have a look at flipboard app on Android. It essentially works like a full-screen app hiding the system bar. But to access the system bar, one doesn't need to move out of the app. If they swipe from top of the screen, the system bar is displayed temporarily overlayed on top of the app.
WindowsPhone UI by default always have the system bar hidden in the interface and it displays only when user swipes from top so essentially this feature of flipboard is an adaptation from there.
This is a good usecase of handling the systembar while also providing maximum real estate to an app and could be a good reference point worth exploring.
Though we could go with full-screen only versus window-mode only versus mixed approach, it is very important to identify the usecase and requirements and decide accordingly.