Why should I use Android Studio, encounter issues and complex tasks for, for example, importing libraries which are developed for Eclipse, having less support about bug I may encounter, ... rather than continuing using Eclipse ?
You should not if you don't want to. You can try this new software or wait for the same on Eclipse platform. See http://tools.android.com/roadmap
Android Studio
- Gradle Build system deep integration
- ADT Feature parity
Eclipse plug-ins
- Visual layout editor
- Resource manager
- Theme editor
- Better refactoring support
That is while Android Studio is pushing with gradle, it is not yet on ADT Feature parity.
What are the real advantages of Android Studio vs Eclipse ?
It is based on other platform: IntelliJ. Eclipse, IntelliJ, NetBeans and other platforms all have their users, features, bugs and plans for development.
So if you starting using Android Studio you should learn from IntelliJ users, that should tell you about those features and how to avoid bugs.
In the end it is just another software to do the same.
Read Is it possible to use the Gradle build system for Android with Eclipse? that have much more links about Android with gradle in Eclipse.
Try Nodeclipse/Enide Gradle for Eclipse
(marketplace) if you want to experiment or fully use as additional build system right now.
Some screenshots for Gradle for Eclipse by Nodeclipse/Enide effort. Like Android Studio it is under development.

