Many of the questions regarding the differences between the two have been covered in a blog post.
The gist of it is that the Android plugin for IntelliJ and Android Studio itself come from the same codebase. New features introduced in Android Studio will be available in IntelliJ as well, if not immediately then soon enough.
Android Studio offers an Android specific development environment with some of the common setup tasks (including Gradle) more streamlined.
IntelliJ is targeted towards developers who do both Android as well as regular Java development. So if you use IDEA for more than just Android development, you are better off sticking with it.