I switched to Android Studio just a couple months ago and the main deficiency I've found compared to Eclipse is that it doesn't auto-build the project on every change so you can immediately see all breakage. I'm constantly hitting "Rebuild Project" because someone decided it couldn't be done for me.
As for advantages over Eclipse, they've been minor. No real big improvements except the automatic dependency management of Gradle.
The reason for the giant effort to switch the entire ecosystem over is a bit mysterious to me.
I believe you can switch that in the settings. Go to Preferences > Build, Execution, Deployment > Compiler and use the checkbox for "Make project automatically".
Likewise, under Compiler there's a "Java Compiler" panel in the hierarchy. You can switch it to using the Eclipse compiler which I think allows you to launch with errors in your project.
For me, IntelliJ's auto-complete is a lot nicer than Eclipse's and that makes me more productive.
However, i've found that i do not notice that so much and get much more benefit from gradle then ant. Also, the project structure has ended up being alot cleaner and easier to navigate for me. Plus, I like all the slick IntelliJ style features.
As for the giant effort to switch? I'd say gradle is a big one.
To be fair, had the ant based build system been written by someone that actually understood ant properly then it wouldn't have been such a mess.
It was also educational just how big a performance difference at code or xml editing existed between ADT and the same Eclipse installation on a vanilla Java project: the latter is like using a machine a decade newer.
The tools people have always had a casual disregard for NDK users too, who make a disproportionately large amount of the Play Store revenue. The whole thing has never seemed like it was dog fooded at all, just developed for amusement.
On *nix, there should be a tool that lets you execute a command whenever files in a certain directory are changed. I did this years ago but forget how I did it.
AFAIK they use Gradle 2.1, which introduced incremental compilation. Unfortunately it's not yet very good at figuring out dependencies. Gradle was never a speed demon to begin with.
As for advantages over Eclipse, they've been minor. No real big improvements except the automatic dependency management of Gradle.
The reason for the giant effort to switch the entire ecosystem over is a bit mysterious to me.