For the time being, Eclipse is the official supported IDE and Android Studio is only available as "Early Access Preview". This means that it's not officially supported yet and that it's only intended for people that want to take a peak on what's to come.
In the table below we show the main differences:
|Eclipse (ADT)||Android Studio|
|Build system||Something internal in the plugin||Gradle|
|Same build as command line||No||Yes|
|Officially supported by Google||Yes||No|
|App flavors possible||No||Yes|
|Reproducible builds||No||Yes (with Gradle)|
|Stability||Not really stable, but workable (mainly because of Eclipse)||Very stable|
At this time I prefer Android Studio. I always use it for personal projects. I don't think it's wise for companies to start using Android Studio. Google is releasing new version almost every week of Android Studio and the Android Gradle plugin. Better to wait for it to get more stable.