Unless libspotify has a particular feature you really need right now, you should not use it. Spotify no longer supports libspotify for Android and will not be releasing and more updates to it. Additionally, libspotify requires you to roll your own native sound driver in JNI, as well as other C++ JNI wrapper code to integrate the library into your project. It's a huge pain and is quite difficult just to get a "hello world" app up and running. Also libspotify on Android has many hard to fix bugs, mostly having to do with native concurrency and threading issues.
Because there are many apps out there using libspotify, we will continue to support the library, at least to the point of making sure that our back end still works with them. However, Spotify does not recommend starting new projects with libspotify.
The new Android SDK (of which I am one of the authors) was specifically designed to fix these shortcomings. Although we had plans to write a Java wrapper around libspotify, we never had the time for it and ended up making the new SDK instead.
That said, the new SDK is lacking some features, such as offline support, but these are being actively worked on and will be fixed in the near future. Also we will be releasing the (almost) full source code for the new SDK, which will make it much easier to debug and contribute to. This was never possible with libspotify for both technical and legal reasons.
