The only advantage for me: you code as fast as formula 1 :). Indeed. If you use Resharper in .NET programming, you will code as fast as in .NET. Even faster.
The bad thing: the lack of some Eclipse tools (a review of my questions ), and it seems that the Eclipse compiler - which you can use from IntelliJ as well - is better. Due to the lack of some tools, you are forced to use many third-party tools.
The bottom line: if you have no problems with Eclipse, then stick with it. I hated the eclipse of Eclipse and why I moved to IntelliJ.
EDIT January 23, 2013
IntelliJ has improved a lot . Now they have a visual UI editor, an excellent connection to the Android SDK, and at the moment I can’t think of any function that Eclipse and IDEA do not have. What's even better, I will say again that IDEA has more features than Eclipse.
EDIT March 11, 2014
IntelliJ has improved again. Thanks to the visual user interface editor for XML layouts and most used as the base for Google Android Studio, it is still the best development environment.
The only drawbacks for the Android developer are IMHO:
it still doesn't fully import the dependencies (libraries), so you need to manually fix the files
it doesn’t recognize other projects (modules) that you sometimes need to add manually.
Google Glass support does not exist
All this has in mind when importing projects executed in Eclipse, which very often happens with someone working on several Android projects.
sandalone Feb 11 '11 at 12:30 2011-02-11 12:30
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