I personally believe one should always use the one which is best and up-to-date. Saying that, Android Studio fits in best as this is the latest development platform with loaded features and easy to use.
The only factor that it takes time and effort for the developers to learn new things. For, developers who starts fresh doesn't make much difference to them as they need to learn either one of the platform and they can start with Android Studio. If one learns Eclipse first, they eventually need to learn Android Studio and upgrade themselves at some point.
Moreover, there are additional features on any new releases than the older version. Similarly, we see some of the well known features that are available on Android Studio and not present in Eclipse, mentioned here:
1. Maven-based build dependencies
2. Build variants and multiple-APK generation (great for Android Wear).
3. Advanced Android code completion and refactoring.
Finally, new and advanced features in these new released platforms helps developers to produce apps faster.