No. There is no fundamental difference.
That said, subclassing android.app.Application is a very good place to store global/state data. There is only one instance and everything that derives from Context has access to it.
I'm also sure that binding a service to an application will result in some odd lifetimes if you aren't careful. What I mean is that even though your app is out of sight and has no activities alive, your application could still exist because your service still exists. Your service still exists because your application still exists. You would have to manually shut down the service based on some event other than onDestroy.