Android Studio uses Gradle as the official build tool for projects, moving away from the now outdated Apache Ant. Gradle is a powerful build tool, especially for Android development with which it's very easy to do things that are otherwise impossible or very hard to do on other build systems,
While the Android team have recently fixed issues that had to do with emulation on an x86 architecture and greatly improving emulator speeds, emulating an Android device and running apps on an ARM architecture is still pretty slow.
Android Studio is the official IDE for Android and it works great as an Android IDE. Unfortunately, that's the only thing it can do, if you want to develop applications for other platforms in Java, you have to learn another IDE as well.
Having to use third-party libraries in Xamarin can be a real pain. Since Xamarin uses C# and third-party libraries are written in Java, you have to create bindings to use them in a Xamarin app. Which is cumbersome and wastes a lot of time. Especially considering that the Xamarin docs are not very...
Google recommends moving away from Eclipse for Android Development, plugins and features are adopted much later from Eclipse than from Android Studio or IntelliJ IDEA and in the future the ADT plugin may be abandoned altogether.