A lot of the debate about whether to move to Android Studio from Eclipse is based around the question of which is better. At the time I wrote this piece (March 2015) the question is somewhat redundant as Android Studio is the official IDE for Android going forward. From that perspective, the decision for me is made. I will be using Android Studio for all new apps and updates for existing apps. The reality for me is that I see no reason to go back to using Eclipse. From my recent experience I have found it difficult update the Eclipse environment free of errors and the effort expended fixing the IDE is simply not worth it. This is particularly true of the v7 appcompat library that has proved to be a problem for me. There are other factors too that makes Android Studio a better choice.
Android Studio supports a wider range of pre-defined emulator devices than the old Eclipse ADT plug-in. I have also found that XXDPI devices are easier to run, taking up less screen space.
Importing Eclipse based projects
I have had no difficulty in importing eclipse based projects. The only issue I have had to address is that some external libraries get missed. I have added a tip to my website to help you address this issue that is easily remedied. See here to fix that.
A key feature of Android Studio is the use of Gradle to build packages. I have noticed inconsistencies being flagged in Android Studio when I have tried to compile a package after being imported into Android Studio. These were not picked up in Eclipse. I have far more confidence that packages produced in Android Studio will be more robust.
Although Android Studio visually looks more complex than Eclipse, I have found it easier to navigate and use than Eclipse. There multiple presentation options for the navigation pane are particularly useful if you want to get a quick view of any missing resource files. The design view of the layout is very accurate compared to the real thing and provides a simple and quick way to check your work across multiple devices without having to run the emulator or drop a package onto a device.
All in all, far more stable and less error prone than Eclipse.