Usually when I develop an application I resize each image to the different densities (ldpi, mdpi, hdpi, xhdpi). However I wonder what difference does it make if I leave the task to the OS by providing only the image for density xhdpi? The graphic result seems the same.
With hdpi and mdpi, you cover most devices. Very few devices have xhdpi yet, less than 1% I believe. And ldpi, forget about ldpi. If you want to only do one density to save you some work, choose hdpi at least, not xhdpi.
If you let the device do its own scaling automatically, especially if you do this on one of the lower end phones, I would guess that it would slow down that phone every time that your application got instantiated.