I would like to have objective answers about this question :
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 ?
What are the real advantages of Android Studio vs Eclipse ?
The last update is now more than a year old, so here goes another update (25th of October 2016):
The only reason I can see for using IntelliJ over Android Studio is if you're using the Ultimate edition. It has a lot more plugins that you can use with the IDE. If you're using the Ultimate edition already and don't want to use two IDE's simultaneously, there is no reason to switch over to Android Studio (except bleeding-edge features).
Android Studio does ship with the C/C++ Plugin now, but AFAIK, there is still no support for HTML/CSS/JS (which is helpful with all these hybrid frameworks these days).
For the sake of keeping this answer short, I have opted to remove all previous (and outdated) statements, instead of just
striking them. Feel free to browse the edit-history if you're interested!