The use of IDE is your personal preference.
But personally if I had to choose, Eclipse is a widely known, trusted and certainly offers more features then Android Studio.
Android Studio is a little new right now. May be it's upcoming versions keep up to Eclipse level soon.
Caution: Android Studio is currently available as an early access preview. Several features are either incomplete or not yet implemented and you may encounter bugs. If you are not comfortable using an unfinished product, you may want to instead download (or continue to use) the ADT Bundle (Eclipse with the ADT Plugin).
My first choice is Android Studio. its has great feature to develop android application.
Eclipse is not that hard to learn also.If you're going to be learning Android development from the start, I can recommend Hello, Android, which I just finished. It shows you exactly how to use all the features of Eclipse that are useful for developing Android apps. There's also a brief section on getting set up to develop from the command line and from other IDEs.
Working with Eclipse can be difficult at times, probably when debugging and designing layouts Eclipse sometimes get stuck and we have to restart Eclipse from time to time. Also you get problems with emulators.
Android studio was released very recently and this IDE is not yet heavily used by developers. Therefore, it may contain certain bugs.
Both are equally good. With Android Studio you have ADT tools integrated, and with eclipse you need to integrate them manually. With Android Studio, it feels like a tool designed from the outset with Android development in mind.
Go ahead, they have same features.