IMO Google made IntelliJ's Android support worse. They added a million items to the menus (like Eclipse), somehow made it slower, replaced IntelliJ's fast and simple project system with Gradle, which is slow and breaks all the time. Bit of a shame really.
IntelliJ doesn't have a dedicated build system. You can choose from no system, Maven, and Gradle.
No system is often good enough for basic projects, but not Android development. Support libraries, configuration, API versions, NDK support, etc. make Gradle a requirement. Gradle is the official build system of Android for a reason, it's not something that Google just added willy-nilly to Android Studio.
As an Android developer, I LOVE Gradle. I think it's a vastly superior build system. I also use it for complex desktop applications, and applications that run on both desktop and Android, using shared code and OS-dependent code (the module system makes this very easy to organize).
Still a million times better than Eclipse though.