I made the switch to Android Studio as fast as I possibly could. There are many things that Ant simply cannot do very well and my alternative was to use a collection of custom python and shell scripts that just weren't very robust or elegant. Seeing the flexibility of gradle was the selling point that tipped the scales.
Upon migrating a larger project with several android library dependencies, I discovered that the current implementation has dog slow compile times. I don't know enough to understand why this is happening, but the situation was untenable. By spending some time with the build system, I've discovered several things that have helped quite a bit.
Part 1: Be A Repo Man
The first thing you should do if your project has lots of libraries is to not have lots of libraries. What I mean by this is that you shouldn't include the entire source for a library if you're not customizing it at all. Many public Android libraries have Maven repositories that offer pre-compiled versions. By switching over, you speed up compile times and simplify your own project. It's also less of a hassle when there's a new release of the library; you just change the version number.
Finding the Maven repo for a public library usually isn't too difficult. The project's home page should have helpful info, and a Google search generally points you in the right direction. Getting the syntax right is a little bit tricky, but a fast and mostly-accurate way to add the dependency to your project is to use Gradle, please. This is also a good opportunity to migrate local jar file dependencies, as long as they also exist in public repos. Make sure you're using the correct version, though. For instance, the popular Guava library has a custom JDK 5 version that you'll need to choose for Android over the most recent release.